John  3"ffett 


"    '  •'"  :    •'  tir    . 


Courst  oi 


NATURAL    PHILOSOPHY, 


FOR 


HIGH  SCHOOLS  AND  ACADEMIES. 


BY 


W.     J.     ROLFE, 

FORMERLY   HEAD   MASTER   OF  THE   HIGH   SCHOOL,   CAMBRIDGE,   MASS., 

AND 

J.     A.     GILLET, 

PROFESSOR   OF   MATHEMATICS   AND   PHYSICS   IN   THE    FEMALE  NORMAL  AND  HIGH 
SCHOOL  OF  THE  CITY  OF  NEW  YORK. 


POTTER,    AINSWORTH,  AND   COMPANY, 
NEW    YORK   AND   CHICAGO. 


Entered  according  to  Act  of  Congress,  in  the  year  1874,  by 

WOOLWORTH,   AINSWORTH,   AND  COMPANY, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


EDUCATION  DEPT, 

By  the  same  Authors. 

CHEMISTRY, 
ASTRONOMY. 

These  books  are  on  the  same  plan  as  this  Natural  Philosophy^  and  the  three 
volumes  form  the  Cambridge  Course  of  Physics. 

Also, 

HANDBOOK  OF  NATURAL  PHILOSOPHY. 
HANDBOOK  OF  CHEMISTRY. 
HANDBOOK  OF  THE  STARS. 

These  are  brief,  elementary  manuals  of  Natural   Philosophy,  Chemistry,  and 
Astronomy,  and  form  a  Shorter  Course  in  Physics. 


PRESS  OF  RAND,  AVERY  &  FRVE,  BOSTON  MASS. 


PREFACE. 


THE  authors  were  led  to  prepare  this  series  mainly  that  they 
might  provide  themselves  with  text-books  containing  an  ele- 
mentary view  of  the  present  state  of  the  Physical  Sciences. 
The  general  plan  and  method  of  the  Course  were  worked  out 
by  Mr.  Gillet,  and  thoroughly  tested  in  the  class-room  by  oral 
teaching,  before  there  was  any  thought  of  publishing  the  books. 

The  authors  felt,  from-  experience,  that  the  elementary  text- 
books on  Physics  now  in  use  are,  as  a  class,  deficient  in  two 
important  particulars.  First,  they  are  sadly  behind  the  times  ; 
and,  secondly,  they  fail  to  give  any  systematic  development  of 
leading  principles.  A  great  revolution  has  taken  place  during 
the  last  twenty-five  years  in  the  departments  of  Chemistry,  Elec- 
tricity, and  Heat.  In  Chemistry  this  revolution  has  been  so 
complete  that  the  present  theories  of  the  science  are  currently 
known  as  "Modern  Chemistry."  The  hypothesis  of  electric 
fluids  has  been  swept  away,  and  Heat  has  been  shown  to  be  a 
mode  of  molecular  motion.  It  is  but  recently  that  Helmholtz 
has  given  the  correct  explanation  of  the  formation  of  the  vowel 
sounds,  of  resultants,  and  of  dissonance  ;  and  that  Tyndall  and 
others  have  investigated  the  subject  of  sounding  and  sensitive 
flames.  In  Optics,  too,  the  cause  of  long  and  short  sightedness, 
and  the  way  in  which  the  eye  adjusts  itself  for  near  and  distant 
objects,  have  been  correctly  understood  only  within  a  few  years. 
In  Astronomy,  also,  the  analysis  of  solar  and  stellar  light  by 
means  of  the  spectroscope  has  led  to  discoveries  of  the  highest 
interest ;  while  recent  investigation  has  thrown  much  light  upon 
the  nature  of  the  photosphere  and  spots  of  the  sun. 

As  the  principles  of  physical  science  are  all  established  by 
facts  of  observation,  the  method  has  been  adopted  in  this  Course 
of  first  establishing  the  fact  by  experiment,  when  this  is  possi- 

54!  ?f»2 


IV  PREFACE, 


^ble,  and  <5£  tjijsht  drawing  out  the  principle.     The  summaries 
'always*  coW  it  thVenjl  of  a  topic,  not  at  the  beginning. 
*t  Tbe'aUt^^8  Relieve  ihat  the  simplest  experiments,  and  those 
'  which*  rfeqirife*  the*  'simplest  apparatus,  are  usually  the  best,  and 
they  have  therefore  sought  to  give  such  experiments  in  all  cases. 

From  their  experience  in  teaching,  the  authors  strongly  rec- 
ommend that  each  lesson  be  explained  and  illustrated  with  the 
class  before  being  given  out  to  be  studied. 

In  preparing  the  present  volume,  the  material  for  the  SOUND 
has  been  drawn  almost  wholly  from  Tyndall's  "  Lectures."  This 
valuable  work  is  now  brought  within  the  reach  of  all  teachers 
by  the  neat  reprint  of  the  Appletons  (New  York,  1867). 

Much  of  the  material  for  the  LIGHT  has  been  taken  from 
Ganot  (Traite  fildmentaire  de  Physique,  I2e  e'dit,  Paris,  1866), 
Herschel  (Familiar  Lectures  on  Scientific  Subjects,  London, 
1867),  and  Potter  (Physical  Optics,  London,  1856). 

In  treating  of  HEAT,  we  have  drawn  mainly  from  Tyndall's 
"Lectures"  and  papers,  and  from  Stewart  (Heat,  Clarendon 
Press  Series,  London,  1867). 

In  ELECTRICITY  we  have  been  greatly  indebted  to  Faraday's 
"  Researches,"  to  Noad's  "  Manual  of  Electricity,  to  Dr.  Fergu- 
son's "  Electricity  "  in  Chambers's  Educational  Course  (Edin- 
burgh, 1866),  and  to  Professor  Cooke's  "  First  Principles  of 
Chemical  Philosophy"  (Cambridge,  1868). 

The  chapter  on  the  PHYSICS  OF  THE  ATMOSPHERE  is  main- 
ly condensed  from  Buchan's  "  Handy  Book  of  Meteorology  " 
(second  edition,  Edinburgh,  1868).  The  teacher  will  do  well  to 
get  this  book,  and  also  Professor  Loomis's  excellent  "  Treatise 
on  Meteorology  "  (recently  published  by  the  Harpers),  to  which 
we  have  once  or  twice  referred. 

CAMBRIDGE,  November  15,  1868. 


TABLE     OF 


PART    FIRST. 
MECHANICS. 

PAGE 

PRESSURE        .        .       .       1;T  V-  .        .        .       ..        .  3 

WEIGHT •  i  ••'$  t. ' •••:  4 

CENTRE  OF  GRAVITY  .       V     V      .'    'v^    ...  6 

SUMMARY         .  '     .  " 12 

PRESSURE  OF  LIQUIDS         .        .        *.      .       .        •        •  13 

SPECIFIC  GRAVITY   .  "     .  '     .       .  x   ....  22 

SUMMARY 24 

PROBLEMS 25 

PRESSURE  OF  GASES 29 

SUMMARY 44 

PROBLEMS     . .45 

MOTION 47 

FIRST  LAW  OF  MOTION 47 

SECOND  LAW  OF  MOTION 50 

FALLING  BODIES 53 

PROBLEMS 55 

THIRD  LAW  OF  MOTION 58 

SUMMARY 62 

PROBLEMS .64 

THE  PENDULUM 65 

SUMMARY 70 

PROBLEMS 71 

MACHINES     AND     SOURCES      OF     MECHANICAL 

POWER 73 

THE  LEVER 73 

THE  WHEEL  AND  AXLE 77 

THE  PULLEY 83 

THE  INCLINED  PLANE         .        .        .        .        .       .        .85 

THE  WEDGE & 

THE  SCREW 87 

SUMMARY «       .       .       «       .  89 


TABLE   OF    CONTENTS. 

: 91 

kfct 92 

HORSE  -PcwE£.  ^ .  *  \ 94 

F/O  ^Vft^D  Pbtv,EJ£  J0*--  V" •  95 

WATER  POWER 96 

STEAM  POWER  .........  100 

SUMMARY no 

PART     SECOND. 
SOUND. 

PAGE 

NATURE   AND   PROPAGATION   OF   SOUND.        .        .  3 

SOUND-WAVES 3 

SUMMARY        .                16 

MUSICAL  SOUNDS 17 

SUMMARY 32 

THE  SUPERPOSITION  AND  INTERFERENCE  OF  SOUND- WAVES   33 

SUMMARY 43 

CHORDS  AND  DISCORDS 44 

SUMMARY 5° 

MUSICAL  INSTRUMENTS 51 

TRANSVERSE  VIBRATION  OF  STRINGS  AND  STRINGED  IN- 
STRUMENTS        .'  •     .        .  51 

SUMMARY '.'        .        .  54 

LONGITUDINAL  VIBRATION  OF  STRINGS,  RODS,  AND  COL- 
UMNS OF  AIR;  AND  WIND  INSTRUMENTS         .        .  55 

SUMMARY 72 

SOUNDING  FLAMES        .      \    •    .       .       v       .        .        •  74 

SUMMARY -    .       .*  'i-;r'rV'     .  79 

THE  HUMAN  VOICE .        .  80 

SUMMARY 82 

THE  HUMAN  EAR.       ...       .       .       .       .       .83 

SUMMARY 86 

CONCLUSION   .        .        .        .        ....        .        .        .87 

LIGHT. 

NATURE   AND   PROPAGATION   OF   LIGHT   .         .        .     91 

RADIATION .        .  91 

SUMMARY  •    ; 96 


TABLE   OF    CONTENTS.  Vll 

REFLECTION  AND  REFRACTION       .       .   \    11^1.1^  %  96 , 

SUMMARY      .        .        .       .       .       .    j   ." J   J.'J  '  . *•    ^.  105 ; 

DISPERSION j   .     A.  j      ,  J1JJJj.l  >  ip^j 

SUMMARY *"*  4 f*j  ***•»;•/ •..?t»«Sl6w:j 

ABSORPTION      ....      v       .       .        .        .  in 

SUMMARY 116 

INTERFERENCE  AND  THE  UNDULATORY  THEORY  OF  LIGHT  116 

SUMMARY      .        .        .        .        .      '." "  "'. "'    .        .        .  127 

DOUBLE  REFRACTION  AND  POLARIZATION      .        •; .     •  I28 

SUMMARY •. "      .  143 

THE  RAINBOW  .       .     * .       .        ,       .        .       .        .  144 

SUMMARY v       .       .       .  147 

OPTICAL   INSTRUMENTS    ."      *     .  .      ^        ,        .        .  148 

LENSES              .       . 148 

SUMMARY      «       ... 152 

THE  EYE 152 

SUMMARY 168 

THE  MICROSCOPE  AND  THE  TELESCOPE.        .        .        .  170 

THE  MAGIC  LANTERN 174 

SUMMARY  . .  176 

MIRRORS 177 

SUMMARY 182 

PHOTOGRAPHY 182 

SUMMARY 187 

CONCLUSION 187 


HEAT. 

NATURE   AND  PROPAGATION   OF   HEAT  .        .        .193 

RADIATION 193 

SUMMARY 201 

ABSORPTION 202 

SUMMARY 212 

EFFECTS  OF  HEAT  ON  BODIES 213 

CONDUCTION -213 

SUMMARY 215 

TEMPERATURE      . 215 

SUMMARY .  222 

CHANGE  OF  STATE 223 

SUMMARY 233 


Vlll  TABLE   OF   CONTENTS. 


•  .........  234 

SUMMARY:'  *•*,.;       .......  240 

'.  .    ;  ........  240 

«•••*!"•*•."       .......  242 

THE  RELATION  OF  WATER  TO  HEAT        ....  243 

SUMMARY  ..........  244 

THERMAL  INSTRUMENTS         ......  245 

SUMMARY         .........  253 

CONCLUSION  ..........  254 

ELECTRICITY. 

MAGNETISM        .........  257 

SUMMARY     ..........  262 

NATURE   AND   SOURCES   OF  ELECTRICITY          .  263 

VOLTAIC  ELECTRICITY         .......  263 

SUMMARY  ..........  276 

RELATIONS  OF  ELECTRICITY  TO  MAGNETISM     .       .        .  277 

SUMMARY         .........  280 

THE  RELATION  OF  ELECTRICITY  TO  HEAT       .       .       .  280 

SUMMARY  .......        ...  284 

FRICTIONAL  ELECTRICITY   .......  285 

SUMMARY         .........  293 

ELECTRICAL  MACHINES   AND   APPLICATIONS  OF 

ELECTRICITY       ........  293 

*  MACHINES  FOR  DEVELOPING  ELECTRICITY     .        .       .  293 

SUMMARY     .        .        .       .       .       .  .       ".        .        .        .  303 

APPLICATIONS  OF  ELECTRICITY      .       .•      .       .       .  304 
SUMMARY      .        .    *   .        .        .       ..'•  '  ...  •      .'       .  "      .318 

CONCLUSION     .......     r\  '     .  318 


APPENDIX  .  .  .  i.  .  ,.  .  .  .  .319 

PHYSICS  OF  THE  ATMOSPHERE 321 

SOURCES  AND  CONVERSION  OF  ENERGY  ....  358 

NOTES  .  . 37° 

QUESTIONS  FOR  REVIEW  AND  EXAMINATION  .  .  .381 

INDEX 399 


THE   ELEMENTS  OF  NATURAL 
PHILOSOPHY. 


THE    ELEMENTS   OF    NATURAL 
PHILOSOPHY. 

I. 

PRESSURE. 

1.  Solids.  —  If  we  take  hold  of  any  part  of  a  stone  and 
lift  it  up,  the  whole  stone  comes  up.      The  parts  of  the 
stone  hold  together  firmly,  so  that  when  one  part  is  moved 
they  all  move  in  a  piece.     Wood,  iron,  lead,  and  many 
other  bodies,  are  like  stone  in  this  respect.     Such  bodies 
are  called  solids. 

2.  Liquids.  —  If  a  goblet  be  filled  with  water  and  slowly 
tipped,  the  water  runs  out,  not  all  together,  but  a  part  at  a 
time.     The  parts  of  the  water  do  not  hold  together  so  firmly 
as  those  of  the  stone.     When  the  water  is  poured  from  the 
goblet,  all  its  parts  do  not  move  in  a  piece,  as  those  of  a 
solid  would  do  were  it  tipped  from  the  same  goblet.    Alco- 
hol, quicksilver,  and  many  other  substances,  resemble  water 
in  this  respect.     Such  substances,  whose  parts  move  easily 
among  themselves,  are  called  liquids. 

3.  Gases.  —  If  water  be  poured  into  a  goblet  from  above, 
it  readily  fills.    If,  however,  a  goblet  be  inverted  and  pressed 
down  upon  water,  it  does  not  fill  with  water.     The  reason 
it  does  not  fill  is,  that  it  is  already  full  of  air.     When  it 
is  inverted   and  pressed   down  upon   the  water,  there   is 
no  chance  for  this  air  to  escape ;    but  when  the  water  is 
poured  in   from   above,  the  air  readily  escapes  from  the 
mouth  of  the  goblet. 


NATURAL  PHILOSOPHY. 


ait  m:  tkfc  goHet  is  quite  unlike  either  a  solid  or  a 
liquid.     Air  and  other  substances  like  it  are  called  gases. 

All  substances  are  called  matter.  There  are,  as  we  have 
seen,  three  states  of  matter,  the  solid,  the  liquid,  and  the 
gaseous. 

4.  Matter  is  acted  upon  by  Gravity.  —  When  a  stone  is 
held  in  the  hand,  it  is  felt  to  press  downward.     There 
is  some  force  drawing  it  towards  the  earth.     This  force  is 
called  gravity. 

WEIGHT. 

5.  The  downward  pressure  which  gravity  causes  a  body 
to  exert  is  called  its  weight. 

When  different  bodies,  as  iron  and  wood,  are  taken  in 
the  hand,  it  is  easy  to  feel  that  some  are  heavier  than  others, 
but  it  is  not  so  easy  to  tell  exactly  how  much  heavier  one 
is  than  another. 

6.  The  Spring  Balance.  —  But  the  weight  of  a  body  may 
be  made  to  bend  a  spring,  and,  when  different  bodies  are 
made  to  bend  the  same  spring,  we  can  readily  tell  how 
much  heavier  one  is  than  another  by  seeing  how  much 


Fig.  i. 


more  it  bends  the  spring.     If  it  bends  the 
©          ©     spring  twice  as  much,  it  is  twice  as  heavy  ; 
=^=1     -— -  and  if  three  times  as  much,  it  is  thrice  as 
heavy.     An  instrument  for  finding  the  weight 
of  a  body  by  seeing  how  much  it  can  bend 
a  spring,  is  called  a  spring  balance.    One  form 
of  this  balance  is  shown  in  Figure   i.     Ii 
consists  of  a  steel  spring  wound  into  a  coil 
One  end  of  this  coil  is  fastened  to  a  ring, 
and  the  other  to  a  hook.     The  body  to  be 
weighed  is  fastened  to  the  hook,  and  the 
whole  raised  by  the   ring.     The  weight  of 
the  body  straightens  or  draws  out  the  spring.     A  pointer 
moving  over  a  plate  in  front,  which  is  divided  into  equal 


NATURAL    PHILOSOPHY.  ',/  i  '*- 


Fig.  2. 


parts,  shows  how  much  the  spring 
A  body  which  will  straighten  the  spring  a  certain  amount 
is  said  to  weigh  a  pound ;  one  which  will  straighten  it 
half  as  much,  half  a  pound ;  one  fourth  as  much,  a 
quarter  of  a  pound  ;  twice  as  much,  two  pounds ;  and 
so  on. 

7.  The  Balance.  —  If  a  straight  rod  be  supported  on  a 
pivot,  in  the  centre,  so  that  it  can  turn  freely,  as  shown  in 
Figure  2,  it  will  remain  level  or  horizontal.    If  now  a  pound 
of  lead  be  hung  from  each  end  of  this  rod,  it  will  still  re- 
main horizontal.     The  two  pieces  of  lead  will  just  balance 
each  other.     If  a  second  pound  of 

lead  be  hung  from  one  end  of  the 
rod,  it  will  require  a  second  pound 
at  the  other  end  to  balance  it.  If 

then  we  have  a  number  of  pieces  of  lead  of  different  sizes, 
whose  weight  is  known,  we  can  readily  rind  the  weight  of 
any  other  body  by  hanging  it  to  one  end  of  the  rod,  and 
adding  the  pieces  of  lead  to  th  e  other  end  till  they  balance 
it.  If  one  pound  of  lead  will  balance  it,  its  weight  is  one 
pound  ;  if  a  quarter  ol  a  pound  of  lead  will  balance  it,  its 
weight  is  a  quarter  of  a  pound  ;  and  so  on. 

An  instrument  for  finding  the  weight  of  a  body  in  this 
way  is  called  a  balance,  and 
the  pieces  of  lead  or  iron 
used  in  weighing  it  are  called 
weights.  A  common  form 
of  the  balance  is  shown  in 
Figure  3.  It  consists  of  a 
bar  turning  on  a  pivot  in 
the  centre,  and  having  pans 

hung  from  each  end  for  holding  the  weights  and  the  body 
to  be  weighed. 

8.  The  Steelyard.- — If  we  have  a  straight  rod  balanced 
like  the  one  above,  with  one  arm  considerably  longer  than 


NATURAL    PHILOSOPHY. 

?!  an&&  weight  of  a  quarter  of  a  pound  is  arranged 
so  that  it  can  slide  along  the  longer  arm,  it  will  be  found, 
on  hanging  a  weight  of  a  quarter  of  a  pound  to  the  end  of 
the  shorter  arm,  that  the  weight  on  the  long  arm  must  be 
placed  just  the  length  of  the  short  arm  from  the  pivot,  in 
order  to  balance  the  weight  on  the  short  arm.  If  a  half- 
pound  weight  be  hung  to  the  short  arm,  the  weight  on  ths 
long  arm  will  have  to  be  placed  twice  the  length  of  the  short 
arm  from  the  pivot,  in  order  to  balance  it.  If  the  weight  on 
the  short  arm  is  three  quarters  of  a  pound,  then  the  weight 
on  the  long  arm  must  be  placed 
three  times  the  length  of  the  short 
arm  from  the  pivot,  to  balance  it ; 
and  so  on.  We  can  then  find 
the  weight  of  a  body  by  hanging 
it  to  the  short  arm,  and  seeing 
how  far  the  weight  on  the  long 
arm  must  be  placed  from  the 
pivot,  to  balance  it. 

An  instrument  for  finding  the  weight  of  a  body  by  this 
method  is  called  a  steelyard.  A  common  form  of  the  steel- 
yard is  shown  in  Figure  4. 


THE   CENTRE    OF   GRAVITY. 

9.  Centre  of  Gravity.  —  In  the  case  of  the  bar  whose 
arms  are  of  the  same  size  and  of  equal  length,  it  has  been 
seen  that,  when  its  centre  is  supported,  the  force  of  gravity 
acting  upon  each  arm  just  balances  that  acting  upon  the 
other.  The  same  is  true  when  one  arm  of  the  bar  is 
twice  as  long  as  the  other,  provided  the  shorter  arm  is 
twice  as  heavy  as  the  longer. 

If  a  circular  disc  of  wood  (Figure  5)  be  pierced  at 
the  centre  and  supported  upon  a  wire,  it  will  remain  at  rest 
in  whatever  way  it  may  be  turned.  In  this  case,  then, 


NATURAL    PHILOSOPHY.  7 

the  force  of  gravity  acting  upon  the  part  of  the  disc  to  the 
right  of  the  support  always  exactly  balances  that  acting  upon 
the  part  to  the  left  of  the  support.  If,  however,  one  part 
of  the  disc  be  loaded  with  lead  or  other  heavy  substance,  it 
will  no  longer  rest  equally  well  in  every  position.  It  will 
now  remain  at  rest  only  when  the  loaded  part  of  the  disc  is 

Fig.  s- 


either  directly  under  or  over  the  support.  It  is  found  on 
trial,  however,  that  there  is  still  a  point  between  the  loaded 
side  and  the  centre,  upon  which  the  disc  will  rest  in  any 
position.  In  this  case  also  it  is  clear  that  the  force  of 
gravity,  acting  upon  the  part  of  the  disc  to  the  right  of  the 
support,  always  exactly  balances  that  to  the  left  of  the  sup- 
port. Such  a  point  can  always  be  found,  whatever  may  be 
the  size  or  shape  of  a  body,  and  of  whatever  material  it 
may  be  made.  This  point  is  called  the  centre  of  gravity. 
The  centre  of  gravity  of  a  body,  then,  is  a  point  such  that 
the  force  of  gravity  acting  upon  the  part  of  the  body  on  one 
side  of  this  point  always  balances  the  force  of  gravity  act- 
ing upon  the  part  on  the  opposite  side,  no  matter  how  the 
body  may  be  placed. 

i  o.  The  Centre  of  Gravity  not  always  in  the  Body  itself.  —  • 
If  a  straight  strip  of  metal  or  wood  be  fastened  to  the  sides 
of  a  ring  so  as  to  pass  through  its  centre,  it  will  be  found 
that  the  ring  will  rest  in  any  position  when  the  centre  is 
supported;  and  that  it  will  not  remain  at  rest  in  every 
position  on  any  other  point.  The  centre  of  gravity,  then, 
of  a  ring  which  is  exactly  alike  throughout  its  whole  extent 
is  at  the  centre  of  the  ring.  If  one  part  of  the  ring  is 
heavier  than  the  other,  the  centre  of  gravity  will  be  found 
to  be  between  the  centre  and  the  heavier  part. 


8  NATURAL    PHILOSOPHY. 

When  two  balls  of  the  same  weight  are  connected  by  a 
straight  rod  (Figure  6)  the  centre  of  gravity  will  be  found 
to  be  at  the  centre  of  the  rod.  If  one  ball  be  twice  as 
heavy  as  the  other,  the  centre  of  gravity  will  be  in  the  rod 
at  a  point  twice  as  near  the  heavier  ball  as  the  lighter 
ball.  If  the  heavier  ball  be  three 

Q        '^          Q    times  the  weight  of  the  Kghte1"  ball> 
the   centre   of  gravity   will   be    thrice 
Q    as  near  this  ball  as  the  other. 

If  the  balls  are  connected  by  a 
curved  rod,  the  centre  of  gravity  will 
no  longer  be  in  the  rod,  but  in  a 
straight  line  which  joins  the  balls.  Its  distance  from 
the  balls  will  be  as  above. 

11.  Equilibrium.  —  If  the  loaded  disc  in  Figure  5  be 
placed   with   its   loaded    part   down,   it   remains   at   rest. 
If  it  be  turned  a  little  either  way  and  then  let  go  again, 
it  returns  at  once  to  its  former  position  of  rest.     If  now 
it  be  carefully  poised  with  the  loaded  side  up,  it  can  be 
made  to  rest;   but  if  we  turn  it  the  least  either  way,  it 
does  not  go  back  to  the  position  of  rest  which  it  has 
just  left,  but  at  once  takes  a  new  position  of  rest  with 
the  loaded  side  down. 

The  disc  a,  which  is  of  the  same  material  throughout, 
remains  at  rest  equally  well  in  any  position. 

When  a  body  is  at  rest  it  is  said  to  be  in  equilibrium. 
When  it  is  at  rest  in  such  a  position  that  on  being  slightly 
disturbed  it  again  returns  to  this  position,  it  is  said  to  be 
in  stable  equilibrium.  When  it  is  at  rest  in  such  a  position 
that  on  being  slightly  disturbed  it  seeks  a  new  position 
of  rest,  it  is  said  to  be  in  unstable  equilibrium.  When  a 
body  remains  at  rest  equally  well  in  any  position,  it  is 
said  to  be  in  indifferent  equilibrium. 

12.  The  Centre  of  Gravity  always  seeks  the  Lowest  Point. 
—  We  have  just  seen  that  when  the  loaded  disc  (Figure 


NATURAL    PHILOSOPHY.  9 

5)  is  in  the  position  b,  if  we  disturb  it  in  the  least  it  falls 
into  the  position  c;  and  that,  if  it  be  moved  from  this 
position  t,  it  will  at  once  return  to  it.  It  will  be  seen 
that,  in  this  position  c,  its  centre  of  gravity  is  lower  than 
in  any  other  position.  And  so  in  every  case  it  will  be 
found  that  the  centre  of  gravity  of  a  body  seeks  the 
lowest  position  which  it  can  take. 

13.  The  Stability  of  Equilibrium.  —  A  sphere  which  is 
of  the  same  material  throughout,  is  in  indifferent  equilib- 
rium (n)  on  a  level  surface,  because  the  centre  of  gravity 
can  fall  no  lower  than  it  is.  If  a  portion  of  the  upper  part 
of  the  sphere  be  removed  by  making  a  hole  there  (Fig- 
ure 7),  the  equilibrium  becomes  sta-  Fig.  7. 
ble,  because  the  centre  of  gravity  is 
brought  below  the  centre  of  the 
sphere,  and  will  have  to  rise  if  the 
sphere  is  moved  either  way.  If  the  upper  part  of  the 
sphere  be  loaded  by  putting  into  the  hole  a  cylinder  which 
more  than  fills  it,  the  equilibrium  becomes  unstable,  be- 
cause the  centre  of  gravity  is  now  brought  above  the  centre 
of  the  sphere,  and  any  motion  either  way  tends  to  lower  it. 

When  a  body  is  so  situated  that  its  centre  of  gravity  is 
raised  by  tipping  it  in  any  direction,  it  is  in  stable  equilib- 
rium ;  when  any  disturbance  of  the  body  tends  to  lower 
its  centre  of  gravity,  it  is  in  unstable  equilibrium  ;  when  on 
being  disturbed  its  centre  of  gravity  neither  rises  nor  falls, 
it  is  in  indifferent  equilibrium. 

In  Figure  8,  ge  shows  the  path  which  the  centre  of 
gravity  g  must  take  when  the  body  is  tipped.  Until  g 
reaches  the  point  e  the  body  tends  to  go  back,  because 
in  so  doing  the  centre  of  gravity  would  fall ;  but  as  soon 
as  g  passes  e  the  body  tends  to  go  over,  because  in  so 
doing  the  centre  of  gravity  would  fall,  h  e  shows  how 
much  the  centre  of  gravity  must  be  raised  to  overturn  the 
body ;  and  this  distance  is  seen  to  be  greater  when  the 
i* 


10 


NATURAL    PHILOSOPHY. 
Fig.  8. 


^  — 


boity  is  resting  on  the  side  a  b  than  when  it  is  resting  on 
the  side  b  c.  It  will  be  found  that  much  more  force  wil) 
be  required  to  overturn  it  in  the  latter  case  than  in  the 
former.  The  more,  then,  the  centre  of  gravity  of  a  body 
has  10  be  raised  in  order  to  overturn  it,  the  more  stable 
its  equilibrium. 

It  will  also  be  seen  from  Figure  8  that  the  broader  the 
base  or'  a  body  compared  with  its  height,  the  more  stable 
its  equilibrium. 

If,  however,  the  body  is  not  upright,  it  may  be  in  un- 
stable equilibrium  even  when  the  base  is  broad.  In  Fig- 
ure 9  ge  is  the  path  which  the  centre  of  gravity  £•  must 

Fig.  9. 


take  when  the  body  abed  is  overturned,  and  it  will  be 
seen  that,  as  soon  as£  is  moved  at  all  in  the  direction  gey 
it  begins  to  fall  and  the  body  will  go  over.  In  the  body 


NATURAL    PHILOSOPHY. 


II 


lm  n  o  the  centre  of  gravity  g  is  not  supported,  and  the 

body  will  fall  over  of  itself. 

It  is   evident,  then,   that  a  body  may  lean  and  yet   be 

in  equilibrium,  provided  the  centre  of  gravity  is  directly 

over  any  point  of  the  base.      If  this  point          Fig.  10. 

be  well  within   the   base,    the   equilibrium 

may  be  very  stable,  as  in  the  case  of  the 

famous  leaning  tower  at  Pisa. 

On  the  other  hand,  a  body  may  be  in 

stable  equilibrium  even  when  the  base   is 

very  narrow.     Thus  a  cork  may  rest  upon 

the  point  of  a  needle,  and  yet  be  in  stable 

equilibrium.     This    may  be  done    by  sticking    two    forks 

into  the  cork,  as  shown  in  Figure  10.    The  forks  bring  the 
Fig.  ii.  centre  of  gravity  below  the   point   of 

support,  so  that  the  cork  cannot  be 
tipped  without  raising  the  centre  of 
gravity.  In  the  same  way,  the  image 
in  Figure  IT  is  balanced  on  its  toe 
by  means  of  the  two  heavy  balls  be- 
neath. So,  too,  in  the  "  prancing 
horse"  (Figure  12)  the  centre  of  grav- 
ity is  brought  below  the  point  of  sup- 
port by  the  leaden  ball  at  the  end  of 
the  curved  rod. 

14.  How  to 
find  the  Centre 
of  Gravity  of  a 

Solid. — When  a  stone,  as  in   Fig- 
ure   13,    is   hung    by  the   cord  A, 

the  centre  of  gravity  must  be  di- 
rectly under  the  point  of  support ; 

that   is,   somewhere    in  the  line  A 

B.     If  the  same  stone  be  hung  by 

the   cord   C,  its  centre  of  gravity 


Fig.  12. 


12 


NATURAL    PHILOSOPHY. 


Fig-  13- 


must   still  be  below  the  point  of  support,  somewhere  in 
the  line   C  D.     Since  the  centre  of  gravity  is  in  both  the 

lines  A  B  and  C  Z>,  it 
must  be  at  the  point  G, 
where  they  cross. 

To  find  the  centre  of 
gravity  of  a  solid,  then, 
suspend  it  from  any 
point  of  its  surface  by 
means  of  a  cord,  and  no- 
tice the  direction  which 
the  cord  takes.  Then 
suspend  it  from  another 
point,  and  again  notice  the  direction  of  the  cord.  The 
point  where  lines  drawn  in  these  directions  would  cross 
each  other  will  be  the  centre  of  gravity. 


SUMMARY. 


Matter  exists  in  three  states.     (1-3.) 

Matter  is  acted  upon  by  gravity.     (4.) 

Gravity  gives  bodies  weight.     (5.) 

The  weight  of  bodies  may  be  found  by  means  of  the 
spring  balance  (6),  the  balance  (7),  or  the  steelyard  (8). 

A  point  can  always  be  found  such  that  the  force  of 
gravity  acting  upon  the  part  of  a  body  to  the  right  of  it  is 
always  balanced  by  the  force  of  gravity  acting  upon  the 
part  to  the  left  of  it,  no  matter  in  what  position  the  body 
may  be  placed.  This  point  is  called  the  centre  of  gravity, 
and  sometimes  lies  within  a  body  and  sometimes  without 
it.  (9,  10.) 

When  a  body  is  at  rest  it  is  said  to  be  in  equilibrium. 
Its  equilibrium  may  be  either  stable,  unstable,  or  indifferent 

(it.) 


NATURAL    PHILOSOPHY.  13 

The  centre  of  gravity  always  seeks  the  lowest  position 
which  it  can  take.  (12.) 

The  stability  of  the  equilibrium  of  a  body  depends  upon 
the  position  of  the  centre  of  gravity,  and  upon  how  much 
it  must  be  raised  to  overturn  the  body.  (13.) 

The  centre  of  gravity  of  a  solid  may  be  found  by  sus- 
pending the  solid  from  two  different  points  of  its  surface 
by  means  of  a  cord.  (14.) 

PRESSURE   OF  LIQUIDS. 

15.  How  to  find  the  Weight  of  a  Liquid.  —  If  a  cup  be 
placed  in  one  pan  of  a  balance  and  weighed,  and  then 
filled  with  water  and  weighed  again,  it  will  be  found  to 
weigh  more  in  the  second  case.     This  shows  that  liquids, 
as   well    as    solids,    are    acted    upon    by   gravity,   which 
causes  them  to  exert  a  downward  pressure.     The  weight 
of  the  water  in  the  cup  is  the  weight  of  the  cup  when 
full  of  water  less  the  weight  of  the  empty  cup.     If  the 
cup  is   filled  with  quicksilver  and  weighed  again,  it  will 
be    found  to   weigh    much   more    than    when   filled   with 
water.      This    experiment   shows   that   some   liquids  are 
heavier  than  others. 

1 6.  Liquids  when  acted  upon  by  Gravity  press,  not  only 
downward,   but  also  upward  and  sideways.  — Fix  a  long 
tube  into  the  top  of  a  wooden  cask,  and  put  a  stop-cock 
into   the   top,    and    another   into    the    side    of   the    cask. 
On  filling  the  cask  and  the  tube  with  water,  and  opening 
the  stop-cocks,  the  water  is   driven   out   of  both.      This 
shows  that  the  water  in  the  cask,  when  acted  upon  by 
gravity,  presses  upwards  and  sideways  as  well  as  down- 
ward. 

The  pressure  which  liquids  exert  sideways  is  called  lat- 
eral pressure. 

17.  The  Upward,  Downward,  and  Lateral  Pressures  are 
equal  for  the  same  Depth  of  Liquid.  —  In  Figure  14  we 


NATURAL    PHILOSOPHY. 

Fig.  14  have  a  glass  vessel,  into  the  top  of 

which  are  inserted  three  glass  tubes 
of  exactly  the  same  size,  with  their 
mouths  at  the  same  distance  from 
the  bottom.  One  of  these  tubes 
opens  downward,  one  upward,  and 
one  sideways.  On  filling  the  vessel 
with  water,  by  means  of  the  funnel, 
the  liquid  rises  to  the  same  height 
in  all  three  tubes.  Now  it  is  the  upward  pressure  which 
causes  it  to  rise  in  the  tube  opening  downward,  the  lat- 
eral pressure  which  causes  it  to  rise  in  the  tube  opening 
sideways,  and  the  downward  pressure  which  causes  it  to 
rise  in  the  tube  opening  upward  ;  and  since  the  tubes 
are  all  of  the  same  size,  and  since  the  water  rises  to 
the  same  height  in  each,  these  pressures  are  all  evidently 
equal. 

The  upward,  downward,  and  lateral  pressures  are  then 
the  same  for  the  same  depth  of  liquid. 

1 8.  The  Upward,  Downward,  and  Lateral  Pressures  of 
a  Liquid  increase  with  the  Depth,  but  are  not  altered  by  tht 
Size  or  Form  of  the  Vessel  which  holds  the  Liquid.  —  The 
more  water  we  pour  into  the  vessel,  in  Figure  14,  the 
higher  the  water  rises  in  the  tubes.  The  upward,  down- 
ward, and  lateral  pressures  increase  with  the  depth  of  the 
liquid. 

If  the  tube  into  which  the  liquid  was  poured  be  re- 
moved from  the  vessel,  and  other  tubes  of  different  sizes 
and  shapes,  but  of  the  same  height,  be  put  in  its  place 
and  filled  with  water,  the  liquid  rises  to  exactly  the 
same  height  in  the  tubes ;  showing  that  the  upward, 
downward,  and  lateral  pressures  of  a  liquid  are  not 
altered  by  the  size  or  shape  of  the  vessel  which  holds 
it. 

For   this   reason,  when  vessels  of  different   sizes   and 


NATURAL    PHILOSOPHY.  15 

shapes  are  connected,  as  shown  in  Figure  15,  if  a  liquid 
be  poured  into  one  of  them  it  will  rise  to  the  same  height 
in  all. 

Fig.  15- 


19.  When  a  dosed  Vessel  is  filled  with  a  Liquid,  and  any 
additional  Pressure  is  brought  to  bear  on  any  Particle  of  this 
Liquid,  every  Particle  is  made  to  exert  the  same  additional 
Pressure,  upward,  downward,  and  sideways.  —  Suppose  the 
four  tubes  in  Figure  14  are  all  of  exactly  the  same  size,  and 
that  the  vessel  is  full  of  water.  Pour  water  into  the  left- 
hand  tube  until  it  rises  to  the  line  c  d.  The  water  rises  in 
all  the  tubes  to  the  same  height.  The  water  poured  into 
the  first  tube  brings  an  additional  pressure  to  bear  upon 
the  particles  of  water  at  its  mouth,  and  it  is  the  additional 
pressure  which  the  particles  at  the  end  of  the  other  tubes 
are  made  to  exert  that  causes  the  water  to  rise  in  them. 
Now  the  water  rises  to  the  same  height  in  all  the  tubes,  and 
since  they  are  all  of  the  same  size  there  must  be  the  same 
number  of  particles  at  the  end  of  each  ;  therefore,  the 
particles  at  the  end  of  the  three  tubes  are  made  to  exert 
the  same  additional  pressure  upward,  downward,  and  side- 
ways, as  that  brought  to  bear  upon  the  particles  at  the 
end  of  the  left-hand  tube. 

At  whatever  depth  these  three  tubes  open,  the  water 
will  be  made  to  rise  in  them  all  to  the  line  c  d,  showing 
that  all  the  particles  of  the  liquid  are  made  to  exert  the 
same  additional  pressure  upward,  downward,  and  sideways. 

That  the  particles  at  different  depths  are  all  made  to 
exert  the  same  additional  upward  pressure  is  shown  by  the 
apparatus  in  Figure  16.  The  three  tubes  b  c  and  d  open 


10 


NATURAL    PHILOSOPHY. 


Fig.  1 6. 


at  different  depths,  and  the  vessel  is  first  filled  with  water, 

which  rises  in  c  and  d  to  the 
line  ef.  Pour  water  into  the 
tube  a  till  it  rises  to  the  line 
gh,  and  it  will  rise  to  the  same 
line  in  all  the  tubes. 

This  explains  the  action  of 
the  hydrostatic  bellows,  repre- 
sented in  Figure  17.  It  con- 
sists of  two  boards  connected  by  a  band  of  leather, 
forming  a  closed  vessel,  and  a  tube  is  in-  Fjg.  17> 
serted  in  the  top  or  at  the  side.  Weights 
are  placed  on  this  board,  and  water  is  poured 
into  the  tube.  As  the  water  fills  the  tube,  the 
board  rises  with  the  weights  upon  it.  If  the 
surface  of  the  board  is  100  times  as  large  as 
the  end  of  the  tube,  one  pound  of  water  in  the 
tube  will  balance  100  pounds  on  the  board. 
As  the  surface  of  the  board  is  100  times  as 
large  as  the  end  of  the  tube,  there  are  100 
times  as  many  particles  of  water  in  contact 
with  the  board  as  there  are  at  the  end  of  the 
tube,  and  as  each  particle  is  made  to  exert 
the  same  pressure,  one  pound  of  water  in  the  tube  ought 
to  balance  100  pounds  on  the  board. 

The  particles  of  a  liquid  under  pressure  act  like  bent 
springs  pressing  equally  in  all  directions.  In  an  open  ves- 
sel, gravity  acting  upon  the  upper  layer  of  particles  makes 
them  press  upon  those  of  the  second  layer,  which  then  act 
like  bent  springs  against  all  their  neighbors,  which  in  turn 
become  as  bent  springs.  In  this  way  the  pressure  of  the 
upper  layer  is  transmitted  equally  throughout  the  whole 
mass.  But  gravity  pulls  down  the  second  layer  as  well  as 
the  first,  and  their  pressure  also  is  transmitted  through  all 
the  mass  below,  so  that  the  third  layer  receives  twice  the 


NATURAL    PHILOSOPHY.  17 

pressure  of  the  second.  In  the  same  way  the  fourth  layer 
receives  three  times  the  pressure  of  the  second ;  and  so  on. 
When  pressure  is  exerted  upon  any  particle  of  a  liquid  in  a 
closed  vessel,  it  is  made  to  act  like  a  bent  spring  upon  all 
its  neighbors,  which  in  turn  act  in  the  same  way  either 
upon  other  particles  or  upon  the  sides  of  the  vessel. 

20.  The  Hydrostatic  Press.  —  It  follows,  from  what  has 
just  been  shown,  that  by  means  of  a  liquid  a  small  pres- 
sure upon  a  small  surface  may  be  made  to  exert  a  great 
pressure  upon  a  large  surface.  In  Figure  18  we  have  two 
cylinders,  with  a  plunger,  or  piston,  in  each.  Suppose  that 

Fig.  18. 


the  surface  of  the  larger  piston  is  thirty  times  that  of  the 
smaller;  if  the  latter  is  pressed  downward  by  a  weight 
of  one  pound,  an  upward  pressure  of  one  pound  will  be 
brought  to  bear  upon  each  portion  of  the  surface  of  the 
large  piston  equal  to  that  of  the  small  piston.  The  whole 
upward  pressure  on  the  large  piston  will  then  be  thirty 
times  the  downward  pressure  on  the  small  one.  If  the 
surface  of  the  larger  piston  had  been  sixty  times  that  of 
the  smaller,  one  pound  on  the  latter  would  have  balanced 
sixty  on  the  former  ;  and  so  on. 

Advantage  is  taken  of  this  fact  in  the  construction  of 
the  hydrostatic  press ;  shown  in  Figures  19  and  20.  The 
two  cylinders  A  and  B  are  connected  by  the  pipe  d. 
The  piston  #,  in  the  small  cylinder  A,  is  worked  by  the 
handle  O,  and  forces  water  into  the  large  cylinder  B, 


NATURAL    PHILOSOPHY. 
Fig.  19. 


where  it  presses  up  the  piston  C.  If  the  end  of  the  pis- 
ton C  is  1,000  times  as  large  as  that  of  the  piston  a,  a 
pressure  of  2  pounds  on  a  would  exert  a  pressure  of  2,000 
pounds,  or  one  ton,  upon  C.  If  a  man  in  working  the 
handle  O  forces  down  the  piston  a  with  a  pressure  of  50 
pounds,  he  would  bring  to  bear  upon  C  a  pressure  of  25 
tons. 

This  press  is  used  for  pressing  cotton,  hay,  cloth,  etc., 
into  bales,  for  extracting  oil  from  seeds,  testing  cannon, 
boilers,  etc.,  and  for  raising  ships  out  of  the  water. 

21.  Springs  and  Artesian  Wells.  —  All  natural  collec- 
tions of  water  illustrate  the  tendency  of  a  liquid  to  find 


NATURAL    PHILOSOPHY. 
Fig.  20. 


its  level.  Thus,  the  Great  Lakes  of  North  America  may 
be  regarded  as  a  number  of  vessels  connected  together, 
and  hence  the  waters  tend  to  maintain  the  same  level  in 
all.  The  same  is  true  of  the  source  of  a  river  and  the  sea, 
the  bed  of  the  river  connecting  the  two  like  a  pipe. 

Springs  illustrate  the  same  fact.  The  earth  is  composed 
of  layers,  or  strata,  of  two  kinds ;  those  through  which 
water  can  pass,  as  sand  and  gravel,  and  those  through 
which  it  cannot  pass,  as  clay.  The  rain  which  falls  on 
high  ground  sinks  through  the  soil  until  it  reaches  a  layer 
of  this  latter  kind,  and  along  this  it  runs  until  it  finds 
some  opening  through  which  it  flows  as  a  spring. 

It  is  the  same  with  Artesian  Wells.  These  wells  derive 
their  name  from  the  Province  of  Artois  in  France,  the  first 
part  of  Europe  where  they  became  common.  It  would 
seem,  however,  that  wells  of  the  same  kind  were  dug  in 
China  and  Egypt  many  centuries  earlier. 

In  Figure  21,  suppose  A  B  and  CD  to  be  two  strata  of 
clay,  and  K K  to  be  a  stratum  of  sand  or  gravel  between 
them.  The  rain  falling  on  the  hills  on  either  side  will 


NATURAL    PHILOSOPHY. 


filter  down  through  this  sand  or  gravel,  and  collect  in  the 
hollow  between  the  two  strata  of  clay  which  prevent   its 


Fig.    21. 


escape.  If  now  a  hole  be  bored  down  to  K K,  the  water, 
striving  to  regain  its  level,  will  rise  to  the  surface  at  Jf,  or 
spout  out  to  a  considerable  height  above  it. 

The  Artesian  well  at  Grenelle,  in  France,  has  a  depth  of 
548  metres,  or  about  1800  feet,  and  the  water  flows  out  at 
the  rate  of  656  gallons  a  minute,  or  nearly  a  million  gallons 
a  day.  One  in  this  country,  at  St.  Louis,  is  2,199  feet  deep, 
and  affords  75  gallons  a  minute. 

22.  A  Body  is  buoyed  up  when  placed  in  a  Liquid.  —  If  a 
stone  be  fastened  to  one  pan  of  a  hydrostatic  balance  and 
weighed  under  water,  it  will  seem  to  be  lighter  than  when 
weighed  in  the  ordinary  manner  in  the  air. 

We  have  already  seen  that  at  the  same  depth  in  a  liquid 
the  upward  and  downward  pressures  just  balance,  but  that 
these  pressures  increase  with  the  depth.  The  bottom  of 
the  stone  in  the  above  experiment  being  deeper  in  the  wa- 
ter than  the  top,  the  upward  pressure  of  the  water  against 
the  bottom  of  the  stone  is  greater  than  the  downward  pres- 
sure of  the  same  liquid  upon  the  top  of  the  stone.  The 
stone  is  accordingly  lifted  up  a  little  when  plunged  under 
water,  and  being  thus  buoyed  up,  seems  to  be  lighter  than 
in  the  air. 


NATURAL    PHILOSOPHY. 


21 


Fig.  22. 


23.  A  Body  is  buoyed  up  in  Water  by  a  Force  just  equal 
to  the  Weight  of  the  Water  which  it  displaces. — In  Figure 
22,  A  is  a  cup  into  which  the  cylinder  B  exactly  fits.  This 
cup  then  will  hold  just  as  much  water  as  B  displaces  when 
under  water.  Hang  this  cup  and  cylinder  to  the  hydro- 
static balance,  and  balance  it  with  weights.  Immerse  the 
cylinder  B  in  a  vessel  of  water,  and  we  find  that  it  is  more 
than  balanced  by  the  weights.  Now,  by  means  of  a  drop- 
ping tube  fill  the  cup  A  with  water 
from  the  vessel.  When  the  cup  is  full, 
the  cup  and  cylinder  are  seen  to  be 
again  just  balanced  by  the  weights. 
This  shows  that  a  body  when  im- 
mersed in  water  is  buoyed  up  by  a 
force  just  equal  to  the  weight  of  the 
water  which  it  displaces. 

It  is  evident  from  this  that,  if  a  solid 
weighs  exactly  as  much  as  the  water  it 
displaces  when  fully  immersed,  it  will 
neither  rise  nor  sink  in  the  water.  If 
it  weighs  more  than  the  water  it  dis- 
places, it  will  sink  ;  if  less,  it  will  rise. 
When  a  body  floats  upon  the  water,  it 
displaces  exactly  its  own  weight  of  wa- 
ter. It  is  well  known  that  a  lump  of 
iron  will  sink,  but  the  same  lump  of 
iron  may  be  hammered  out  into  a  ves- 
sel which  will  displace  its  own  weight  of  water  without 
being  wholly  immersed. 

In  this  way,  ships  may  be  made  of  iron  which  will  float 
upon  water  as  well  as  ships  made  of  wood. 


22  NATURAL    PHILOSOPHY. 

SPECIFIC     GRAVITY. 

24.  Substances  vary  in  Density.  — When  the  same  bulks 
of  different  solids  and  liquids  are  weighed,  their  weights 
are  found  to  be  very  different.     A  substance  which  weighs 
more,  bulk  for  bulk,  than  another  substance  is  said  to  be 
more  dense,  or  to  have  a  greater  density.     It  is  often  desira- 
ble to  know  the  relative  weights  of  the   same  bulks    of 
bodies  which  vary  in  density.     In   such  cases,  it  is  con- 
venient to  compare  the  weight  of  each  substance  with  the 
weight  of  the  same  bulk  of  some  given  substance.     Water 
is  taken  as  the  substance  with  which  the  weights  of  other 
solids  and  liquids  are  compared.     The  weight  of  a  given 
substance  compared  with  the  weight  of  the  same  bulk  of 
water,  is  called  its  specific  gravity. 

25.  Specific  Gravity  of  Solids. — To   find    the   specific 
gravity  of  a  solid  or  liquid,  we  must  know  the  weight  of 
the  substance  and  that  of  the  same  bulk  of  water. 

The  weight  of  the  solid  can  be  found  in  the  ordinary 
way.  The  weight  of  a  bulk  of  water  equal  to  that  of  the 
solid  can  then  be  found  by  weighing  the  solid  in  water,  and 
subtracting  its  weight  in  water  from  its  weight  in  air. 
The  difference  of  these  weights  is,  as  we  have  seen  (23), 
just  equal  to  the  weight  of  the  water  it  displaces,  and  this 
is,  of  course,  a  bulk  of  water  just  equal  to  its  own  bulk. 

26.  Specific  Gravity  of  Liquids.  —  The  specific  gravity  of 
liquids  is  most  conveniently  found  by  means  of  an  instru- 
ment, shown  in  Figure  23,  called  a  hydrometer.     It  consists 
of  a  hollow  glass  cylinder,  with  a  stem  and  scale-pan  above, 
and  a  small  bulb  filled  with  mercury  below,  by  which  it  is 
made  to  float  upright  in  a  liquid.    The  instrument  is  placed 
in  water,  and  weights  are  added  until  it  sinks  to  a  point 
marked  upon  the  stem.      The  weight  of  the  hydrometer, 
together  with  the  weights  in  the  pan,  is  equal  to  the  weight 
of  the  water  displaced  (23).     If  now  the  instrument  be 


NATURAL   PHILOSOPHY.  23 

placed  in  another  liquid  whose  density  is  not  the  same  as 
that  of  water,  as  alcohol,  and  made  to  sink  by  weights  to 
the  mark  on  the  stem,  the  weight  of  an  equal  bulk  of  that 
liquid  can  be  found.  The  specific  gravity  of  the  liquid  will, 
of  course,  be  the  weight  of  the  liquid  divided  by  the  weight 
of  the  water. 

Fig.  23.  Fig.  24. 


A  more  common  form  of  hydrometer  is  shown  in  Figure 
24.  It  consists  of  a  glass  tube  and  bulb  loaded  with  mer- 
cury at  the  bottom.  This,  when  put  into  a  liquid  in  which 
it  will  float,  always  displaces  just  its  own  weight  (23). 
It  is  first  put  into  pure  water,  and  the  point  to  which  it 
sinks  is  marked  upon  the  stem.  If  it  be  now  put  into 
a  liquid  of  less  density,  it  will  sink  deeper;  if  into  one 
of  greater  density,  it  will  not  sink  so  deep.  By  means  of 
the  scale  on  the  stem,  the  specific  gravity  of  the  liquid 
into  which  it  is  put  is  indicated.* 

*  See  Appendix,  I. 


24  NATURAL    PHILOSOPHY. 


SUMMARY. 

Liquids  have  weight  as  well  as  solids  (15).  When  acted 
upon  by  gravity  they  press  upward,  downward,  and  side- 
ways (16). 

The  upward,  downward,  and  lateral  pressures  are  always 
equal  for  the  same  depth  of  the  liquid  (17). 

These  pressures  increase  with  the  depth  of  the  liquid,  but 
are  not  altered  by  the  size  or  shape  of  the  vessel  which  holds 
the  liquid  (18). 

When  any  pressure  is  brought  to  bear  upon  one  particle 
of  a  liquid,  every  particle  of  the  liquid  is  made  to  press 
with  the  same  force  upward,  downward,  and  sideways  (19). 

On  this  account,  when  a  small  force  acts  upon  a  few  par- 
ticles of  a  liquid,  an  enormous  force  may  be  brought  to 
bear  on  a  large  surface  in  contact  with  the  same  liquid. 
Advantage  is  taken  of  this  fact  in  the  construction  of  the 
hydrostatic  press  (20). 

Springs  and  Artesian  wells  illustrate  the  tendency  of  wa- 
ter to  seek  a  level  in  connected  vessels  (21). 

A  body  is  buoyed  up  in  water  by  a  force  equal  to  the 
weight  of  the  water  which  it  displaces  (22,  23). 

The  specific  gravity  of  a  solid  or  liquid  is  the  weight  of 
the  solid  or  liquid  compared  with  the  weight  of  the  same 
bulk  of  water  (24). 

To  find  the  specific  gravity  of  a  solid  or  a  liquid,  we 
must  know  the  weight  of  the  substance  and  that  of  the 
same  bulk  of  water. 

The  weight  of  a  bulk  of  water  equal  to  that  of  the  solid 
can  be  found  by  weighing  the  solid  in  air  and  in  water 


The  specific  gravity  of  a  liquid  may  be  found  by  means 
of  a  hydrometer  (26). 


NATURAL    PHILOSOPHY.  25 

PROBLEMS. 

WEIGHT    OF    LIQUIDS. 

1.  A  glass  flask  when  full  of  water  weighs  180  grammes.* 
The  flask  itself  weighs  84  grammes.     How  many  grammes 
of  water  does  the  flask  hold  ? 

2.  The  same  flask  when  full   of  mercury  weighs  1382 
grammes.     How  many  grammes  of  mercury  does  it  hold  ? 

3.  The  same  flask  full  of  alcohol  weighs  160  grammes. 
How  many  grammes  of  alcohol  does  it  hold  ? 

4.  The  same  flask  full   of  sulphuric  acid  weighs   220 
grammes.     How  many  grammes  of  sulphuric  acid  does  it 
hold? 


THE  PRESSURE  WHICH  LIQUIDS  EXERT  BY  REASON 
OF   THEIR    WEIGHT. 


In  these  problems  it  is  assumed  that  in  liquids  the 
pressure  increases  at  exactly  the  same  rate  as  the  depth. 

5.  When  water  is  one  centimetre  deep  in  a  vessel  it  ex- 
erts a  pressure  of  one  gramme  on  every  square  centimetre 
of  surface  at  the  bottom  of  the  vessel.    What  would  be  the 
pressure  exerted  upon  every  square  centimetre  of  surface 
at  the  bottom,  if  the  water  in  the  vessel  were  3  centimetres 
deep  ? 

6.  What  would   be  the  pressure  upon  9   square  deci- 
metres  of  surface   at   the   bottom,  if  the   liquid   were   6 
centimetres  deep  ? 

7.  What  upon  13  square  decimetres  at  the  bottom,  if 
the  liquid  were  17  centimetres  deep? 

8.  A  closed  vessel  is  3  decimetres  deep,  and  has  a  tube 
projecting  from  the  top  to  the  height  of  one  metre.     The 
bottom  of  the  vessel  has  a  surface  of  50  square  decimetres, 

*  See  French  Weights  and  Measures,  p.  lid. 


26  NATURAL    PHILOSOPHY. 

and  the  vessel  is  filled  with  water  to  the  top  of  the  tube. 
What  is  the  whole  pressure  upon  the  bottom  of  the 
vessel  ? 

9.  What  would  be  the  pressure  upon  a  square  centimetre 
of  surface  on  the  side  of  the  above  vessel,  the  centre  of  the 
surface  being  3  centimetres  from  the  bottom  ? 

10.  What  would  be  the  pressure  upon  a  square  centi- 
metre of  surface  at  the  top  of  the  vessel  ? 

n.  What  would  be  the  pressure  upon  the  whole  upper 
surface  of  the  vessel,  supposing  it  to  contain  50  square 
decimetres  ? 

12.  A  cubical  vessel,  every  side  of  which  is  a  square 
metre,  is  filled  with  water.     What  would  be  the  pressure 
upon  its  bottom  ? 

13.  What   would    be    the    pressure    upon    each  of    its 
sides  ?  * 

14.  Suppose  the  top  of  the  above  vessel  were   closed 
and  a  tube   one   metre   in   length   were  inserted    into  it, 
on  filling  the  tube  to  the   top  what  would  be  the  pres- 
sure exerted  upon  the  top  of  the  vessel  ? 

15.  What  would  be  the  pressure  upon  the  bottom  of  the 
vessel  when  the  tube  is  full  of  water  ? 

1 6.  What  would  be  the  pressure  upon  the  sides  of  the 
vessel  in  the  last  case  ? 

THE    HYDROSTATIC    PRESS. 

17.  The  end  of  the  small  piston  in  a  hydrostatic  press 
has  a  surface  of  10  square  centimetres ;  and  the  end  of  the 
large  piston  a  surface  of  a  square  decimetre.     A  pressure 
of  10   kilogrammes  upon   the   small   piston  would  bring 
what  pressure  to  bear  upon  the  large  piston? 

*  To  find  the  pressure  upon  any  surface  at  the  sides  of  a  vessel, 
take  the  average  depth  of  the  surface,  that  is,  the  distance  from  the 
top  of  the  water  to  the  middle  of  that  surface. 


NATURAL    PHILOSOPHY.  27 

1 8.  If  the  small  piston  be  the  same  as  above,  and  the 
2nd  of  the  large  piston  contain  a  square  metre  of  surface, 
5  kilogrammes  upon  the  small  piston  will  cause  what  pres- 
sure to  be  brought  to  bear  upon  the  end   of  the   large 
piston  ? 

19.  A  pressure  of  75  kilogrammes  on  the  small  piston 
would  cause  what  pressure  to  be  exerted  upon  the  end  of 
the  large  piston  ? 

THE    BUOYANCY   OF  LIQUIDS. 

$ip"  A  cubic  centimetre  of  water  weighs  one  gramme. 

20.  A  body  weighs  50  kilogrammes  in  air,  and  has  a 
bulk  of  40  cubic  decimetres.     How  much  does  it  weigh 
in  water? 

21.  A  stone  weighs  80  kilogrammes  in  the  air,  and  55 
kilogrammes  in  water.     What  is  its  bulk  ? 

22.  A  hollow  vessel  of  copper  weighs  one  kilogramme. 
What  must  be  its  bulk  in  order  that  it  may  just  float  in 
water  ? 

23.  A  hollow  vessel  of  iron    weighs    15    kilogrammes. 
What  must  be  its  bulk  in  order  that  it  may  sink  one  half 
in  water  ? 

24.  A  boat  displaces  12  cubic  metres  of  water.     What 
is  its  weight  ? 

SPECIFIC   GRAVITY. 

25.  A  body  weighs  150  hectogrammes  in  air,  and  weighs 
2  kilogrammes  in  water.     What  is  the  weight  of  a  bulk  of 
water  equal  to  that  of  the  body  ? 

26.  A  flask  full  of  water  weighs  62  grammes  :  a  piece 
of  lead  weighs  44  decagrammes  in  the  air.     It  is  put  into 
the  flask,  and  the  flask  is  filled  with  water.     It  is  found 
that   the   lead    and  water   together  weigh    462    grammes. 
What  is  the  weight  of  a  bulk  of  water  equal  to  that  of 
the  lead  ? 


28  NATURAL    PHILOSOPHY. 

27.  A  piece  of  lead  weighs  56  grammes  in  the  air,  and 
51   grammes  in  water.     What  is  the   specific   gravity  of 
lead? 

28.  A  flask   holds   75   grammes  of  water :    a  lump  of 
copper,  which  weighs  160  grammes  in  the  air,  is  put  into 
the  flask,  and  it  is  found  that  the  water  and  the  copper 
together  weigh  219  grammes.     What  is  the  specific  gravity 
of  copper? 

29.  The  specific   gravity  of  iron  is  7.8.     What  weight 
of  water  will  45  kilogrammes  of  iron  displace  ? 

30.  The  specific  gravity  of  zinc  is  7.2.     What  is  the 
bulk  of  90  kilogrammes  of  zinc  ? 

31.  A  piece  of  wood,  which  weighs  25  grammes  in  the 
air,   is   fastened  to  a  piece  of  iron  whose  weight  is   80 
grammes ;    and  on  immersing  both  in  water  and  weighing 
them,  it  is  found  that  they  together  weigh  45   grammes. 
What  is  the  weight  of  the  water  displaced  by  the  wood  ? 

32.  A  piece  of  wood,  weighing  42  grammes,  is  fastened 
to  a  piece  of  zinc  weighing  86  grammes,  and  both  are 
weighed  under  water,  and  are  found  to  weigh  34  grammes. 
What  is  the  specific  gravity  of  the  wood  ? 

33.  A  flask  weighing  20  grammes  weighs  430  grammes 
when  full  of  water,  and  5555  grammes  when  full  of  mer- 
cury.    What  is  the  specific  gravity  of  mercury  ? 

34.  A   hydrometer   weighing   50   grammes   requires   a 
weight  of  80  grammes  to  sink  it  to  the  neck  in  water,  and 
a  weight  of  135  grammes  to  sink  it  to  the  same  depth  in 
sulphuric  acid.     What  is  the  specific  gravity  of  sulphuric 
acid? 

35.  A  vessel  holds   100  kilogrammes  of  water.     How 
much  mercury  would  it  hold? 

36.  How  much  alcohol  will  it  hold,  if  the  specific  gravity 
of  alcohol  is  .79  ? 


NATURAL    PHILOSOPHY.  29 


THE   PRESSURE   OF   GASES. 

27.  Gases  have  Weight. — Weigh  very  carefully  a  thin 
copper  globe  when  filled  with  air;    then  exhaust  the  air 
from  it  by  means  of  the  air-pump,  and  again  weigh  it.     It 
will  be  found  to  weigh  less  in  the  last  case  than  at  first. 
This  shows  that  air  has  weight.     In  like  manner,  it  may 
be  shown  that  all  gases  have  weight 

28.  Gases ;  like  Liquids,  press   upward,  downward,  and 
sideways.  —  Fasten  over  the  mouth  of  a  bell-jar,  open  at 
both  ends  (Figure  25),  a  piece  of  india-rubber,  and  place 

Fig.  25. 


the  bell-jar  on  the  plate  of  the  air-pump,  and  exhaust  the 
air  from  under  the  rubber.  The  rubber  will  be  forced  into 
the  jar,  showing  the  downward  pressure  of  the  air.  If  a 
bell-jar,  with  its  mouth  at  the  side,  be  closed,  as  before, 
with  a  piece  of  india-rubber,  on  exhausting  the  air  from 
the  jar  the  rubber  is  forced  into  it.  This  shows  the 
lateral  pressure  of  the  air.  If  the  neck  of  the  jar  is  bent 
around  still  farther,  so  that  it  shall  open  downward,  and 
the  mouth  is  closed  as  before,  on  exhausting  the  air  the 
rubber  is  forced  into  the  jar.  This  shows  the  upward 
pressure  of  the  air. 

29.  The  Hand-Glass.  —  If  the  first  bell-jar  in  Figure  25 
is  small  enough  at  the  top  to  be  covered  with  the  palm 
of  the  hand,  and  the  air  be  exhausted  from  it  when 
thus  covered,  the  hand  will  be  held  down  with  consider- 
able force  by  the  pressure  of  the  air  upon  it. 


NATURAL    PHILOSOPHY. 


If  a  wet  bladder  be  tied  over  the  same  bell-jar  and  dried, 
and  the  air  be  exhausted  as  before,  the  bladder  will  burst 
with  a  loud  noise.  These  two  experiments  show  the  down- 
ward pressure  of  the  air. 

30.   The  Magdeburg  Hemispheres.  —  Figure  26  represents 


Fig.  27. 


Fig.  26. 


two  brass  hemispheres,  some  four  inches  in  diameter,  the 
edges  of  which  are  made  to  fit  tightly  together.  The  whole 
can  be  screwed  to  the  air-pump  by  means  of  the  stop- 
cock at  the  bottom.  While  the  hemispheres  contain  air, 
they  can  be  separated  with  ease,  since  the  outward  pressure 
is  just  balanced  by  the  inward  pressure  ;  but  when  the  air 
within  is  pumped  out,  it  is  very  hard  to  pull  them  apart. 
Since  it  is  equally  difficult  to  do  this,  in  whatever  position 
the  hemispheres  are  held,  the  experiment  shows  that  the 
air  presses  in  all  directions. 

This  piece  of  apparatus  is  called  the  Magdeburg  Hemi- 
spheres, from  Otto  von  Guericke,  of  Magdeburg,  by  whom 
it  was  invented. 


NATURAL    PHILOSOPHY. 


31.  The   Weight  Lifter.  —  In  Figure  28,  A  is   a  strong 
glass    cylinder,    open    at    both 

ends ;  B  a  piston,  working  air- 
tight within  it ;  and  C  a  brass 
plate,  covering  it  closely,  and 
having  a  hole  in  the  centre  to 
which  a  hose  may  be  screwed 
for  connecting  it  with  the  air- 
pump.  When  the  air  is  ex- 
hausted from  the  cylinder,  the 
piston  rises,  even  if  a  heavy 
weight  is  hung  from  it  as  shown 
in  the  Figure. 

This  experiment  affords  a 
very  striking  illustration  of  the 
upward  pressure  of  the  air. 

32.  The  Expansive  Force  of  Gases.  —  If  an  india-rubber 

bag,  partially  filled  with  air,  be  closed 
air-tight  and  placed  under  the  re- 
ceiver of  the  air-pump,  the  bag  fills 
out,  as  shown  in  Figure  29,  when  the 
air  is  exhausted  from  the  receiver. 
The  same  would  be  true  if  the  bag 
were  partially  filled  with  any  gas. 
All  gases  then  tend  to  expand. 

33.  The  Air-Pump.  —  An  instttb 
ment  for  removing  the  air  from  a  vessel  is  called  an  air- 
pump.  One  form  of  such  a  pump  is  shown  in  Figure  30. 
It  consists  of  a  cylinder,  in  which  a  piston  moves  air-tight. 
In  this  piston  is  a  valve  opening  upward.  At  the  top  of 
the  cylinder  is  another  valve  also  opening  upward.  The 
bottom  of  the  cylinder  is  connected  with  the  pump-plate 
by  means  of  a  tube.  On  this  plate  is  placed  the  vessel 
from  which  the  air  is  to  be  exhausted.  This  vessel  is  called 
che  receiver.  The  piston  is  worked  by  means  of  the  handle. 


32  NATURAL    PHILOSOPHY. 

As  the  piston  is  forced  down  the  expansive  force  of  the  ail 
below  pushes  open  the  valve  in  the  piston  to  get  into  the 
space  left  behind  it.  When  the  piston  is  drawn  up  again 
the  expansive  force  of  the  air  above  closes  this  valve  and 
opens  the  valve  at  the  top  of  the  cylinder,  so  that  this  air 
escapes.  The  expansive  force  of  the  air  in  the  tube 

Fig.  30- 


and  receiver  causes  it  to  fill  the  space  behind  the  piston. 
When  the  piston  is  again  pushed  down,  the  downward 
pressure  of  the  air  outside  closes  the  valve  at  the  top  of 
the  cylinder,  while  the  expansive  force  of  the  air  below 
opens  the  valve  in  the  piston,  and  some  of  the  air  passes 
through  it.  On  drawing  up  the  piston  again  this  air  is 
removed  as  before.  By  continuing  this  process  the  air 
is  nearly  all  withdrawn  from  the  receiver.  It  cannot  be 
wholly  withdrawn,  because  as  it  becomes  more  and  more 
exhausted,  the  expansive  force  becomes  less  and  less,  until 
at  last  it  is  not  sufficient  to  open  the  valve  in  the  piston. 


NATURAL    PHILOSOPHY. 


33 


34.  A  Body  is  buoyed  up  in   the  Air.  —  If  a   hollow 
sphere  be  balanced  in  the  air  by  a  piece  of  lead,  and  then 
the  whole  apparatus  be  put  under  the  receiver  of  an  air- 
pump  and  the  air  exhausted,  the  lead  will  no  longer  bal- 
ance the  sphere.     This  shows  that  a  body  is  buoyed  up 
in  the  air  as  well  as  in  a  liquid  (22).     Bodies  seem  to  be 
lighter  in  the  air  than  in  a  vacuum  (that  is,  a  space  from 
which  the  air  has  been  exhausted),  for  the  same  reason  that 
a  body  seems  lighter  in  water  than  in  the  air.    The  upward 
pressure  of  the  air  upon  the  bottom  of  the  body  is  some- 
what greater  than  the  downward  pressure  upon  the  top  of 
the  body.     A  body  in  the  air,  then,  is  buoyed  up  by  a  force 
just  equal  to  the  weight  of  the  air  which  it  displaces.     If  a 
body  weighs  more  than  the  air  it  displaces,  it  sinks  through 
the  air ;  if  it  weighs  less  than  the  air  it  displaces,  it  rises  in 
the  air. 

35.  Balloons.  —  Balloons  rise  in  the  air  because  they  are 
filled  with  some  substance  which  makes  them  lighter  than 
the  air  which  they  displace. 

If  a  glass  bulb  and  tube  filled  with 
air  be  arranged,  as  in  Figure  31,  with 
the  end  of  the  tube  under  water,  and 
the  bulb  be  heated  by  means  of  a 
lamp,  the  air  in  it  expands,  and  a 
part  of  it  is  driven  out  in  bubbles 
through  the  water.  This  shows  that 
air  expands  when  heated. 

Paper  balloons  are  sometimes  made  which  are  sent  up 
by  fastening  a  light  just  under  an  opening  in  the  bottom  of 
the  balloon.  The  light  heats  the  air  inside,  and  causes  it 
to  expand,  and  a  part  to  pass  out.  The  remainder  is  then 
lighter  than  the  air  displaced  by  the  balloon,  and  it  con- 
sequently rises.  Large  balloons  are  made  of  strong  silk, 
and  filled  with  some  very  light  gas,  such  as  coal  gas. 
This  makes  the  balloon  so  much  lighter  than  the  air 

2*  C 


Fig.  31- 


34 


NATURAL    PHILOSOPHY. 


Fig.  32. 


it  displaces,  that  it  will  rise,  carrying  a  car  with  two  or 
three  persons  in  it. 

Balloon  ascensions  are  now  quite  common,  and  it  is 
possible  that  the  time  will  come  when  by  their  aid  we  may 
navigate  the  air  as  we  now  navigate  the  sea.  As  yet,  how- 
ever, it  has  been  found  impossible  to  guide  them.  When 
once  in  the  air  they  are  at  the  mercy  of  the  wind,  and  go 
in  whichever  way  it  happens  to  be  blowing. 

36.   The  Atmospheric  Pressure  will  sustain  a  Column  of 

Liquid  in  an  inverted  Vessel. 
—  If  a  glass  jar  be  filled  with 
water  and  inverted  in  a  dish 
of  water,  care  being  taken  to 
keep  the  mouth  of  the  jar 
all  the  time  under  water, 
the  liquid  will  not  flow  out 
of  the  jar  when  it  is  raised. 
If,  however,  the  jar  be  par- 
tially filled  with  water,  and 
inverted  in  a  shallow  dish 
of  water,  and  placed  un- 
der the  receiver  of  an  air- 


pump, 


and    the  air   be    ex- 


hausted, the  water  will  flow 
out  from  the   jar  ;    showing 
that   it  is   the   pressure    of 
the  atmosphere  on  the  sur- 
face of  the  water  in  the  dish 
which  keeps  the  water  in  the 
inverted  jar.     If  mercury  or 
alcohol   is   used    instead  of 
water,  the  result  is  the  same. 
37.    The  Atmospheric  Pressure  will  sustain   a    Column 
of  Mercury  about  30  Inches  high.  —  If  a  glass  tube  closed 
at   one   end   and   about    34   inches   long  be   filled   with 


NATURAL    PHILOSOPHY.  35 

mercury,  and  inverted  in  a  cup  of  mercury,  as  shown 
in  Figure  32,  a  part  of  the  mercury  will  run  out,  leaving 
a  column  about  30  inches  high  in  the  tube. 

38.  The  Atmospheric  Pressure  is -equal  to  about  15  Pounds 
to  the  Square  Inch.  —  Suppose  the  tube  in  the  above  ex- 
periment were  one  inch  square,  it  follows,  from  the  way 
in  which  liquids  press,  that  the  downward  pressure  at  the 
bottom  of  the  tube  would  be  just  equal  to  the  downward 
pressure  of  the  atmosphere  on  each  square  inch  of  the 
surface  of  the  mercury  in  the  vessel. 

If  now  we  weigh  the  mercury  in  the  tube,  we  shall  find 
that  there  are  about  15  pounds  of  it.  This  column  of  mer- 
cury then  exerts  a  pressure  of  15  pounds  at  the  bottom 
of  the  tube.  The  air  then  presses  with  a  weight  of  15 
pounds  upon  every  square  inch  of  surface.  We  do  not 
perceive  this  great  pressure,  because  the  air  presses  equally 
in  every  direction. 

39.  The  Atmospheric  Pressure  varies  from  Day  to  Day. 
—  If  a  glass  tube  be  filled  with  perfectly  pure  mercury,  so 

that  it  shall  not  become  tarnished,  and  then  inverted  in  a 
cup  of  mercury  and  left  standing,  and  the  height  of  the 
mercury  column  noted  from  day  to  day,  it  will  be  found 
to  vary  considerably,  being  sometimes  as  much  as  two 
inches  higher  than  at  other  times.  This  variation  in  the 
height  of  the  mercury  column  must  be  due  to  changes  in 
the  pressure  of  the  air. 

40.  The  higher  the  Place,  the  less  the  Atmospheric  Pres- 
sure. —  If  the  height  of  the  mercury  in  the  tube  be  noticed 
at  the  base  of  a  mountain,  and  it  be  then  carried  to  the 
top  of  the  mountain  and  the  height  of  the  mercury  again 
noticed,  it  will  be  found  considerably  less  in  the  latter 
case.     This  shows  that  the  atmospheric  pressure  becomes 
less,  the  higher  we  go  above  the  surface  of  the  earth. 

The  atmosphere  is  a  great  ocean  of  air  which  surrounds 
the  earth,  and  at  the  bottom  of  which  we  live,  as  the  fishes 


36  NATURAL    PHILOSOPHY. 

live  at  the  bottom  of  the  sea.  The  changes  in  the  height 
of  the  mercury  just  described  show  that  the  pressure  in 
creases  with  the  depth.  The  daily  variations  in  the  pres- 
sure are  probably  due  to  large  waves  which  run  over  the 
surface  of  this  ocean. 

41.  The  Barometer.  —  An  instrument  for  measuring  the 
pressure  of  the  atmosphere  is  called  a  barometer.  One 
form  of  it  is  shown  in  Figure  33.  It  consists 
of  a  cup  and  tube  filled  with  mercury,  as  in  the 
experiment  illustrated  by  Figure  32.  These 
are  fastened  to  a  wooden  frame.  At  the  up- 
per part  of  the  tube  there  is  a  scale  with  a 
sliding  index,  for  measuring  the  height  of  the 
mercury.  H  is  a  thermometer. 

The  mercury  is  often  put  into  a  leather  bag 
instead  of  an  open  cup  as  here,  since  it  is  less 
likely  to  be  spilled.  As  the  leather  is  flexible 
the  pressure  of  the  air  is  brought  to  bear  upon 
the  mercury  through  the  bag. 

42.  Uses  of  the  Barometer.  —  It  has  already 
been  stated  that  the  atmospheric  pressure  is 
less  as  the  height  above  the  earth  is  greater. 
When  we  have  found  at  what  rate  it  dimin- 
ishes, we  can  readily  find  the  height  of  moun- 
tains by  means  of  the  barometer.  We  have 
to  find  the  difference  between  the  readings  of 
the  barometer  at  the  level  of  the  sea  and  at 
the  top  of  the  mountain.  This  shows  how 
much  the  pressure  has  diminished,  and  from 
this  we  can  find  the  height  of  the  mountain. 

The  barometer  is  also  of  considerable  use 
in  indicating  the  approach  of  storms,  espe- 
cially of  violent  winds.  It  has  been  observed 
that  such  storms  are  very  likely  to  occur  im- 
mediately after  a  sudden  diminution  of  atmos- 


NATURAL    PHILOSOPHY.  37 

pheric  pressure,  which  is  shown  by  a  rapid  fall  of  the  mep 
cury  in  the  barometer  tube.  On  the  other  hand,  a  gradual 
rise  of  the  mercury  in  the  tube  usually  indicates  the  ap- 
proach of  fair  weather. 

The  mere  height  of  the  mercury  in  the  tube  tells  us  little 
about  the  weather,  but  a  careful  study  of  the  movements 
of  the  mercury  enables  us  to  judge  pretty  accurately  what 
changes  are  likely  to  occur  in  the  weather. 

43.  Pumps.  —  As  water  is  somewhat  more  than  thirteen 
times  lighter  than  mercury,  the  pressure  of  the  atmosphere 
will  sustain  a  column  of  this  liquid  about  thirteen  times 
thirty  inches  in  height,  or  considerably  more  than  thirty 
feet.  If  the  tube  is  open  at  the  top  it  is  necessary  to  re- 
move the  air  from  it  before  the  water  will  rise  into  it.  An 
instrument  for  raising  water  in  this  way  is  called  a  pump. 

The  common  lifting-pump  is  shown  in  Figure  34.  It  is 
really  an  air-pump,  with  piston  and  valves  like  those  de- 
scribed above  (33),  and  it  works  in  the  very  same  way. 
When  the  piston  P  is  forced  down,  the  air  below  it,  by  its 
expansive  force,  opens  the  valve  O,  through  which  it  es- 
capes. When  the  piston  is  drawn  up  again,  the  valve  O 
is  kept  shut  by  the  pressure  of  the  air  above,  and  the  air 
in  A  expands,  pushes  open  the  valve  *S,  and  rushes  into 
the  vacuum  above.  The  air  being  thus  partly  removed 
from  A,  the  pressure  of  the  air  upon  the  water  in  the  well 
outside  is  greater  than  that  inside  the  pipe,  and  conse- 
quently forces  the  water  up  the  pipe  and  through  the  open 
valve  S.  When  the  piston  is  pushed  down  again,  the  pres- 
sure of  the  water  in  the  cylinder  shuts  the  valve  S,  and 
opens  the  valve  O.  The  water  thus  gets  above  the  piston, 
which  on  going  up  again  lifts  it  so  that  it  flows  out  at  the 
spout,  as  shown  in  the  figure. 

Figure  35  represents  the  force-pump.  In  this  pump  the 
piston  P  is  solid.  When  it  is  drawn  up,  the  water  below 
by  its  upward  pressure  opens  the  valve  S  and  fills  the 


38  NATURAL    PHILOSOPHY. 

Fig.  34-  Fi&  35- 


cylinder.  When  the  piston  is  pushed  down,  the  valve  S 
being  shut  by  its  own  weight  and  the  pressure  of  the  water 
upon  it,  the  water  is  forced  up  through  the  valve  O  into 
the  pipe  D.  When  the  piston  goes  up  again,  the  valve  O 
is  closed  by  its  own  weight  and  that  of  the  water  above, 
the  valve  6"  opens,  and  the  cylinder  is  filled  as  before. 

In  Figure  36  we  have  these  two  pumps  combined.  The 
air  is  pumped  out  through  the  valves  S  and  O,  and  the 
water  is  forced  up  into  the  cylinder  through  the  pipe  A 
and  the  valve  S,  just  as  it  was  in  the  lifting. pump ;  and 
the  water  is  then  forced  through  the  valve  O  and  the  pipe 
D)  as  in  the  force-pump  just  described. 


NATURAL    PHILOSOPHY. 


39 


In  both  these  forms  of  force-pump  the  water  is  driven  out 
of  the  pipe  D  only  when  the  piston  is  going  down.  It  may 
be  made  to  flow  out  in  a  steady  stream  by  adding  an  air- 
chamber  above  the  valve  O,  as  shown  in  Figure  37.  As 


Fig.  36. 


Fig.  37. 


the  water  is  forced  into  this  chamber  it  compresses  the  air, 
which  by  its  expansive  force  exerts  a  continuous  pressure  on 
the  water,  and  drives  it  in  a  constant  stream  up  the  pipe. 

In  the  fire-engine,  two  force-pumps  are  usually  connected 
with  one  air-chamber.  The  pumps  are  so  arranged  that 
the  piston  of  one  is  going  down  while  that  of  the  other  is 
going  up,  thus  forcing  water  into  the  air  chamber  all  the 
time. 

44.  The  Siphon.  —  Bend  a  tube  into  the  form  of  the  let- 
ter [/,  making  one  arm  somewhat  longer  than  the  other  ; 
fill  it  with  water,  and  close  each  end  with  the  fingers ;  then 
invert  it  and  place  the  short  end  under  the  surface  of  wa- 
ter in  a  vessel.  If  now  both  ends  are  opened,  the  water 
will  flow  out  of  the  vessel  through  the  tube.  A  bent  tube 
used  in  this  way  is  called  a  siphon. 

To  explain  the  action  of  a  siphon,  let  us  suppose  it 


NATURAL   PHILOSOPHY. 


Fig.  38. 


filled  and  the  short  arm  placed  in  the  water.  The  pressure 
then  acting  on  C  (Figure  38),  and  tending  to  raise  the  wa- 
ter in  the  tube,  is  the  atmospheric  pressure  less  the  weight 
of  the  column  of  water  CD.  In  like  manner,  the  pressure 

on  the  end  of  the  tube  B 
is  the  atmospheric  pressure 
less  the  pressure  of  the 
column  of  water  A  B.  But 
as  this  latter  column  is 
longer  than  CD,  the  force 
acting  at  B  is  less  than  th% 
force  acting  at  (7,  and  con> 
sequently  the  water  will  be 
driven  through  the  tube  by 
a  force  equal  to  the  differ- 
ence of  these  two  forces. 
The  flow  will  therefore  be 
the  faster,  as  the  difference 
of  level  between  C  and  B  is  greater. 

45.  Tantalus's  Cup. — This  is  a  glass  cup,  with  a  siphon 
tube  passing  through  the  bottom,  as  shown  in  Figure  39. 
If  water  be  poured  into  the  cup,  it  will  rise  both  inside  and 
outside  the  siphon  until  it  has  reached  the  top  of  the  tube, 
when  it  will  begin  to  flow  out.  If  the  water  runs  into  the 
Fi  cup  less  rapidly  than  the  siphon 

carries  it  out,  it  will  sink  in  the 
cup  until  the  shorter  arm  no 
longer  dips  into  the  liquid  and 
the  flow  from  the  siphon  ceases. 
The  cup  will  then  fill  again  as 
before  ;  and  so  on. 

In    many    places     there    are 
springs  which  flow    at   intervals, 
like   the   siphon   in    this    experi- 
ment, and  whose  action  may  be  explained  in  the  same 


NATURAL    PHILOSOPHY.  4! 

way.  A  cavity  under  ground  may  be  gradually  filled  with 
water  by  springs,  and  then  emptied  through  an  opening 
which  forms  a  natural  siphon.  In  some  cases  of  this  kind 
the  flow  stops  and  begins  again  several  times  in  an  hour. 

46.  The  Air-Gun  and  the  Condenser.  —  We  have  seen 
that  gases  exert  an  expansive  force  which  increases  when 
they  are  heated  (35).      It  increases  also  when  they  are 
compressed  into  smaller  space.     This  is  illustrated  by  the 
air-gun,  which  consists  of  a  tube  connected  by  a  stop-cock 
with  a  small  air-tight  vessel  of  very  great  strength.     If  a 
large  amount  of  air  be  forced  into  this  vessel,  and  the 
stop-cock  be  then  opened,  the  expansive  force  of  the  con- 
fined gas  will  drive  a  bullet  from  the  tube  as  if  it  were 
fired  from  a  musket. 

The  firing  of  a  musket  is  in  fact  another  illustration  of 
the  very  same  kind.  When  the  gunpowder  is  set  on  fire  it 
forms  an  immense  amount  of  gas,  which,  being  condensed 
into  a  small  space,  has  a  very  great  expansive  force,  and 
therefore  exerts  a  very  great  pressure  upon  the  bullet. 

An  instrument  used  for  compressing  air  in  this  and 
other  experiments  is  called  a  condenser.  It  consists  of  a 
strong  cylinder  with  a  piston  and  valves  arranged  precisely 
as  in  the  force-pump  in  Figure  35.  It  works  too  in  the 
same  way  as  the  force-pump ;  the  air  rushing  in  through 
the  valve  6*  when  the  piston  is  raised,  and  being  driven 
out  through  the  valve  O  when  the  piston  is  pushed  down. 
The  vessel  into  which  the  air  is  to  be  forced  is  screwed  to 
the  pipe  D. 

47.  Mariotte's  Law.  —  In   Figure  40  we    have  a   long 
glass  tube  closed  at  one  end  and  bent  up  into  the  form  of 
the  letter  U.      Pour  in  a  little  mercury,  and  tip  the  tube  a 
little,  so  that  a  part  of  the  air  may  escape  from  the  closed 
end,  and  the  mercury  may  stand  at  the  same  level  in  both 
arms.     The  column  of  air  in  the  closed  arm  is  now  evi- 
dently under  a  pressure  equal  to  that  of  the  atmosphere, 


42  NATURAL    PHILOSOPHY. 

which  we  have  seen  to  be  equal  to  that  of  a  column  of 
mercury  30  inches  high  (37).  If  now  mercury  be  poured 
into  the  long  arm  until  its  level  in  that  arm  is  30  inches 
above  that  in  the  short  arm,  the  air  in  this  arm  will  be 
under  a  pressure  of  two  atmospheres, 
or  30  pounds  to  the  square  inch.  Un- 
der this  pressure  it  will  be  seen  that 
the  column  of  air  is  just  half  as  long 
as  it  was  before.  If  more  mercury  be 
poured  in,  until  its  level  in  the  long 
arm  is  60  inches  above  that  in  the 
short  arm,  then  the  air  in  the  short 
arm  will  be  under  a  pressure  of  three 
atmospheres,  or  45  pounds  to  the 
square  inch;  and  it  will  be  found  to 
be  only  one  third  as  long  as  at  first 
When,  therefore,  the  pressure  upon  a 
column  of  air  is  doubled,  the  bulk 
is  reduced  to  one  half;  when  it  is 
trebled,  the  bulk  is  reduced  to  one 
third;  and  so  on. 

The  fact  that  the  bulk  of  a  gas  be- 
comes less  just  in  proportion  as  the 
pressure  upon  it  becomes  greater,  or, 
in  other  words,  that  the  volume  of  a 
gas  is  inversely  as  the  pressure  which  it 
bears,  is  called  Mariotte's  law,  from  its 
discoverer. 

In  the  above  experiment,  it  is  evi- 
dent that  when  the  bulk  of  the  air  has  been  reduced 
to  one  half,  its  expansive  force,  or  its  elasticity,  has  been 
doubled,  since  it  balances  double  the  pressure  in  the  long 
arm  that  it  did  before.  When  its  bulk  is  reduced  to 
one  third,  it  balances  thrice  the  pressure;  and  so  on. 
The  elasticity  of  a  gas  then  becomes  greater  just  in  pro- 


NATURAL    PHILOSOPHY. 


43 


portion  as  its  bulk  becomes  less,  or  as  the  pressure  upon 
it  becomes  greater ;  or,  in  other  words,  the  elasticity  of  a 
gas  is  inversely  as  its  volume,  and  directly  as  the  pressure 
which  it  bears. 

48.  The  Manometer.  —  An  instrument  for  measuring  the 
expansive  force,   or  pressure,  of  a  gas  is 

called  a  manometer.  One  form  of  the  ma- 
nometer is  shown  in  Figure  41.  It  consists 
of  a  glass  tube  closed  at  the  upper  end  and 
filled  with  air.  Its  lower  end  is  fastened 
into  a  small  iron  box  containing  mercury. 
The  tube  A  serves  to  connect  the  box  with 
the  closed  vessel  holding  the  gas  whose  ex- 
pansive force  is  to  be  tried.  The  height  to 
which  the  mercury  is  raised  by  the  pressure 
of  the  gas  is  shown  by  a  scale. 

49.  The  Spirit  Level.  —  If  a  tube  be  filled 
with  liquid  except  a  mere  bubble  of  air, 
and  then  closed,  this  bubble  will  always 
rise  to   the    highest  part  of  the   tube,   in 
whatever  position  it  may  be  placed.     Ad- 
vantage is  taken  of  this   fact  in  the  con- 
struction of  the  spirit  level. 

The  most  common  form  of  this  instru- 
ment (Figure  42)  consists  of  a  closed  glass  tube,  AB, 
very  slightly  curved  on  the  upper  side.  It  is  filled  with 
spirit,  with  the  exception  of  a  bubble  of  air  which  tends 


Fig.  42. 


cj 


;D 


to  rise  to  the  highest  part  of  the  tube.  It  is  placed  in  a 
case  CD,  which  is  so  arranged  that  when  it  is  placed  on 
a  perfectly  level  surface  the  bubble  of  air  is  exactly  in 
the  middle  of  the  tube,  as  represented  in  the  figure. 


44  NATURAL    PHILOSOPHY. 


SUMMARY. 

Gases  have  weight.     (27.) 

Gases,  like  liquids,  press  upward,  downward,  and  side- 
ways.    (28.) 

These  pressures  of  gases  are  illustrated  by  the  hand-glass, 
the  Magdeburg  hemispheres,  and  the  weight-lifter.  (29-31.) 

Gases  are  acted  upon  by  an  expansive  force.       (32.) 

The  air  can  be  exhausted  from  a  vessel  by  means  of  the 
air-pump.  (33.) 

Bodies  are  buoyed  up  in  air  by  a  force  equal  to  the 
weight  of  the  air  which  they  displace.  (34.) 

It  is  owing  to  this  that  balloons  rise  in  the  air.     (35.) 

The  atmospheric  pressure  balances  a  column  of  mercury 
about  thirty  inches  high,  and  is  equal  to  about  fifteen 
pounds  to  the  square  inch.  (37,  38.) 

This  pressure  varies  from  day  to  day,  and  becomes  less 
as  the  height  of  the  place  increases.  (39,  40.) 

The  barometer  is  an  instrument  for  measuring  the  at- 
mospheric pressure.  (41.) 

It  is  used  in  finding  the  height  of  mountains,  and,  to  a 
certain  extent,  it  indicates  changes  of  the  weather.  (42  ) 

The  action  of  pumps  is  to  be  explained  by  the  pressure 
of  the  atmosphere.  (43.) 

The  siphon  also  acts  by  reason  of  the  atmospheric 
pressure.  (44.) 

The  expansive  force,  or  elasticity,  of  gases  is  increased 
by  heat  and  by  pressure.  (46.) 

The  bulk  or  volume  of  a  gas  is  in  the  inverse  ratio  of 
the  pressure  which  it  bears. 

The  elasticity  of  a  gas  is  in  the  inverse  ratio  of  its  votume^ 
or  the  direct  ratio  of  the  pressure  it  bears. 

These  facts  are  known  as  Mariotte's  law.     (47.) 

The  elasticity  of  gases  is  measured  by  means  of  the 
manometer.  (48.) 


NATURAL    PHILOSOPHY.  45 

PROBLEMS. 
WEIGHT    OF    GASES. 

The  specific  gravity  of  a  gas  is  its  weight  compared 
with  that  of  an  equal  bulk  of  atmospheric  air. 

37.  A  glass  globe  of  the  capacity  of  one  litre  weighs 
83  grammes  after  the  air  has  been  exhausted  from  it ;  and 
84.292  grammes  when  full  of  air.     What  is  the  weight  of 
\  litre  of  air  ? 

38.  The  same  globe,  when  full  of  ammonia  gas,  weighs 
83.759  grammes.     What  is  the  weight  of  a  litre  of  ammo- 
nia gas  ? 

39.  The    same    flask,    when    full    of   carbonic    acid, 
weighs  84.964  grammes.     What  is  the  weight  of  a  litre 
of  carbonic  acid? 

40.  The  same  flask,   full  of  hydrogen,  weighs  83.089 
grammes.     What  is  the  weight  of  a  litre  of  hydrogen  ? 

41.  The  same  flask,  when  full  of  oxyyen,  weighs  84.428 
grammes.     What  is  the  weight  of  a  litre  of  oxygen  ? 

42.  What  is  the  specific  gravity  of  ammonia  gas  ?    What 
is  the  specific   gravity  of  carbonic   acid  ?     What   is    the 
specific  gravity  of  hydrogen  ?     What  is  the  specific  gravity 
of  oxygen  ? 

43.  A  vessel  of  the  capacity  of  985  litres  would  hold 
how  many  grammes  of  air  ?     Of  carbonic  acid  ? 

44.  A  vessel  of  the  capacity  of  416  litres  would  hold 
how  many  grammes  of  hydrogen  ?     Of  oxygen  ? 

PRESSURE    CAUSED    BY    THE    WEIGHT   OF   GASES. 


The  atmospheric  pressure  is  about  one  kilogramme 
upon  every  square  centimetre  of  surface  at  the  level  of 
the  sea. 

45.  The  body  of  an  ordinary-sized   man  has  a  surface 
of  about    16,000    square   centimetres.      How  many  kilo- 


46  NATURAL    PHILOSOPHY. 

grammes  of  pressure  does  the  atmosphere  exert  upon  a 
man's  body  ?     How  many  pounds  avoirdupois  ? 

46.  A  room  is  12  metres   long,  9  metres  wide,  and  5 
metres  high.     How  many  kilogrammes  of  pressure   does 
the  atmosphere  exert  upon  the  floor  of  the  room  ?     How 
many  pounds  ? 

47.  How  many  kilogrammes  of  pressure  does  it  exert 
upon  each  end  of  the  room  ? 

48.  How  many  on  each  side  ? 

49.  How  many  kilogrammes  of  air  does  the  room  contain? 

50.  The  atmospheric  pressure  will  balance  a  column  of 
mercury  76  centimetres  high,  and  the  specific  gravity  of 
mercury  is  13.5.     It  will  balance  a  column  of  water  how 
many  centimetres  high  ?     How  many  feet  high  ? 

51.  If  water  is  to  be  raised  1,200  centimetres  high  by 
means  of  the  lifting   pump,   how  much  of  this  distance 
must  the  water  be  lifted  ? 

52.  Water  is  to  be  carried  over  a  hill  1,350  centimetres 
high.     Can  it  be  done  by  means  of  the  siphon  ?     Why  ? 

BUOYANCY   OF  GASES. 

53.  A  block  of  wood  has  a  bulk  of  900  cubic  metres- 
How  much  is  it  buoyed  up  in  the  air  ? 

54.  A  balloon  when  filled  with  gas  weighs  500  kilo 
grammes.     How  many  litres  of  bulk  must  it  have  in  order 
that  it  may  just  float  in  the  air  ? 

55.  A  balloon  has  a  bulk  of  1,000  cubic  metres,  ana 
weighs  25  kilogrammes.     It  is  filled  with  coal  gas,  whose 
specific  gravity  is  .6.     By  how  many  kilogrammes  of  pres- 
sure is  it  forced  upward  ?     If  a  car,  which,  with  all  its  fix- 
tures, has  a  bulk  of  3  cubic  metres  and  weighs  48  kilo- 
grammes, be  attached  to  the  balloon,  with  what  pressure 
will  the  whole  be  forced  upward  ? 


NATURAL    PHILOSOPHY.  47 

II. 

MOTION. 

WE  have  now  studied  somewhat  the  pressures  produced 
by  gravity  and  other  forces  acting  upon  the  three  states  of 
matter.  We  have  seen  that  when  a  stone  is  held  in  the 
hand  it  presses  upon  it ;  and  it  is  well  known  that  on  re- 
moving the  hand  the  stone  falls  to  the  ground.  We  are 
now  to  study  the  motions  caused  by  gravity  and  other 
forces. 

FIRST  LAW   OF  MOTION. 

It  is  a  well-known  fact  that  a  stone  or  other  body, 
when  at  rest,  will  not  begin  to  move  of  itself,  but  only  on 
the  application  of  some  force.  It  is  equally  well  known 
that  when  any  body,  such  as  a  ball,  is  in  motion,  it  requires 
some  force  to  stop  it. 

50.  A  moving  Body  when  left  to  itself  will  always  move 
in  a  straight  Line  and  at  the  same  Rate.  —  If  a  heavy  weight, 
such  as  a  lead  ball,  be  suspended  from  a  point  by  means  of 
a  string  or  a  wire,  and  it  be  set  swinging,  it  will  swing  for 
a  time  and  then  come  to  rest.  A  ball  thus  suspended  is 
called  a  pendulum.  If  this  pendulum  be  placed  under  the 
receiver  of  an  air  pump,  and  the  air  partly  exhausted,  it 
will  swing  a  longer  time ;  and  the  more  the  air  is  exhausted 
the  longer  the  pendulum  will  swing.  If  the  pendulum  be 
nicely  hung,  so  that  there  will  be  very  little  friction  at  the 
point  on  which  it  turns,  it  will,  when  once  set  going  in  an 
exhausted  receiver,  swing  24  or  30  hours.  Since  the  length 
of  the  time  that  the  pendulum  will  swing  increases  as  the 
resistance  it  meets  diminishes,  we  conclude  that  it  would 
swing  forever,  provided  there  were  no  resistance  to  its  mo- 


48  NATURAL    PHILOSOPHY. 

tion.  Now,  mathematicians  have  found  that  they  can  ex- 
plain this  swinging  of  the  pendulum  by  supposing  that  the 
ball  of  the  pendulum,  wheri  once  put  in  motion,  would 
move  on  forever  in  a  straight  line  and  at  the  same  speed, 
were  it  not  acted  upon  by  any  other  force.  They  have 
found,  moreover,  that  this  is  the  only  way  in  which  they 
can  explain  the  motion  of  the  pendulum. 

We  conclude,  then,  that  a  moving  body  when  left  to  it- 
self will  always  move  in  a  straight  line  and  at  the  same 
rate.  This  is  usually  called  \htfirst  law  of  motion. 

The  inability  of  a  body,  whether  at  rest  or  in  motion, 
to  change  its  state,  is  often  called  inertia. 

51.  An  unbalanced  Force  must  act  upon  a  Body  in  order  to 
put  it  in  Motion,  or  to  change  the  Direction  or  the  Rate  of 
its  Motion.  —  A  ball  held  in  the  hand  remains  at  rest,  be- 
cause the  downward  pull  of  gravity  upon  the  ball  is  just 
balanced  by  the  resistance  offered  by  the  hand.  If  the 
hand  is  removed  so  that  the  force  of  gravity  is  unbalanced, 
then  the  ball  begins  to  move.  If  we  push  with  the  hands 
against  the  opposite  sides  of  a  book,  the  book  will  remain 
at  rest  as  long  as  the  push  of  one  hand  is  just  balanced  by 
that  of  the  other.  Take  away  one  hand,  so  that  there  shall 
be  nothing  to  balance  the  push  of  the  other,  and  the  book 
begins  to  move.  So,  in  every  case,  a  body  begins  to  move 
only  when  an  unbalanced  force  acts  upon  it. 

And  when  a  body  is  once  in  motion,  it  changes  the  di- 
rection and  rate  of  its  motion  only  when  an  unbalanced 
force  is  acting  upon  it.  When  a  body  is  once  in  motion  it 
is  just  as  natural  for  it  to  continue  to  move  in  a  straight 
line,  with  uniform  speed,  as  it  is  for  it  to  remain  at  rest  when 
once  it  is  at  rest.  It  seems  to  us  more  natural  for  a  body 
to  be  at  rest,  because,  when  a  body  is  put  in  motion  at  the 
surface  of  the  earth,  it  always  meets  with  resistance  which 
quickly  brings  it  to  rest  again,  unless  the  moving  force 
continues  to  act  upon  it. 


NATURAL    PHILOSOPHY.  49 

52.  The  Effect  of  a  Force  acting  for  a  Moment  only. — 
When  the  moving  force  acts  upon  a  body  only  an  instant, 
as  when  a  ball  is  struck  with  a  bat,  or  a  bullet  is  fired 
from  a  gun,  it  has  its  greatest  speed  at  first,  and  its  motion 
is  gradually  wasted  by  the  resistance  it  meets  in  passing 
through  the  air  or  over  the  earth. 

53.  The  Effect  of  a  Force  acting  continuously.  —  When, 
however,  a  body  is  acted  upon  continuously  by  a  force,  as 
in  the  case  of  a  railway  train  or  a  steamboat,  the  motion, 
slow  at  first,  gradually  increases  till  it  reaches  a  certain 
point,  when  the  speed  remains  unchanged  so  long  as  the 
moving  force  is  unchanged.     When  the  moving  force  is  in- 
creased the  speed  increases,  and  when  it  is  diminished  the 
speed  diminishes. 

54.  The  Resistance  a  Moving  Body  meets  increases  as  the 
Square  of  its    Velocity.  —  The  steamboat  in  moving  has  to 
push  aside  a  certain  amount  of  water  in  a  second,  and  this 
is  the  chief  resistance  it  meets.     Now,  as  the  speed  of  the 
boat  increases,  more  water  must  be  pushed  aside  in  a  sec- 
ond, and  each  particle  of  water  must  be  moved  aside  more 
quickly.     Hence,  the  faster  it  moves,  the  greater  the  resist- 
ance.    Suppose  the  speed  of  the  boat  to  be  doubled,  twice 
as  many  particles  of  water  must  be  pushed  aside  in  a  sec- 
ond, and  each  particle  must  be  pushed  aside  in  half  the 
time.      Hence,  the  resistance  becomes  fourfold  when  the 
velocity  is  doubled.     The  resistance,  then,  increases  as  the 
square  of  the  velocity.     This  explains  the  fact  that,  in  or- 
der to  double  the  speed  of  a  steamboat,  the  power  of  the 
steam  must  be  quadrupled,  and  in -order  to  treble  the  speed 
the  power  must  be  increased  ninefold.     The  same  is  true 
in  the  case  of  the  train  of  cars,  or  of  any  moving  body. 
When  their  velocity  is  doubled,  they  meet  resistance  at 
twice  as  many  points  in  a  second,  and  the  resistance  at 
each  point  must  be  overcome  in  half  the  time. 

55.  A  moving  Body  may  be  in  Equilibrium.  — We  have  seen 

3  D 


50  NATURAL    PHILOSOPHY. 

(n)  that  a  body  at  rest  is  in  equilibrium.  It  is  so  be- 
cause the  forces  acting  upon  it  are  balanced.  In  the  case 
of  a  train  of  cars,  on  first  starting  the  force  of  the  steam 
is  not  wholly  balanced  by  the  resistance  ;  hence  it  imparts 
motion  to  the  train.  But  as  the  speed  of  the  train  in- 
creases, the  resistance  also  increases,  until  it  finally  equals 
the  force  of  the  steam.  All  the  force  of  the  steam  is  now 
used  in  balancing  the  resistance,  and  the  speed  no  longer 
changes.  Since  the  two  forces  acting  upon  the  moving 
body  balance  each  other,  it  must  be  in  equilibrium.  Every 
body  then  moving  in  a  straight  line  and  with  uniform  speed 
is  in  equilibrium. 

SECOND   LAW   OF  MOTION. 

56.  A  Force  has  the  same  Effect  in  producing  Motion,  whether 
it  acts  upon  a  Body  at  Rest  or  in  Motion,  and  whether  it  acts 
alone  or  with  other  Forces.  —  In  Figure  43,  A  B  is  a  board  ; 

Fig.  43- 


CD  an  arm  moving  upon  it,  turning  on  a  hinge  at  C,  and 
driven  by  a  spring  E ;  at  the  end  of  the  arm  D  is  a  hol- 
low, with  its  opening  in  the  side  of  the  arm  large  enough  to 
contain  a  small  ball,  so  that  when  the  arm  is  driven  by  the 
spring  E,  the  ball  will  be  thrown  horizontally ;  at  F  is  an- 


NATURAL   PHILOSOPHY.  51 

other  chamber  opening  downwards,  the  lower  opening  being 
closed  by  the  board  G,  which  will  be  knocked  away  by  a 
blow  of  the  arm  CD.  If  a  ball  be  put  in  the  chamber  at  D, 
and  another  in  the  chamber  at  Fy  the  very  same  movement 
which  throws  the  first  horizontally  forward  will  let  the  sec- 
ond drop  at  the  same  instant.  On  trying  the  experiment 
it  will  be  found  that  both  balls  will  reach  the  floor  exactly 
together.  So,  too,  if  the  machine  and  floor  are  both  in- 
clined at  just  the  same  angle,  the  balls  will  both  reach  the 
floor  together. 

In  the  case  of  the  ball  that  is  thrown  horizontally,  two 
forces  have  acted,  one  to  throw  it  forward  in  a  straight  line, 
and  the  other  to  draw  it  to  the  earth  in  a  straight  line  ; 
and  it  is  seen  that  it  is  drawn  just  as  far  towards  the  earth 
in  a  given  time  as  the  ball  that  was  let  fall  from  a  state  of 
rest. 

From  this  and  other  experiments  it  has  been  found  that, 
when  two  forces  acting  in  different  directions  have  been 
brought  to  bear  upon  a  body  so  as  to  produce  motion,  the 
body  at  any  given  time  will  be  just  as  far  from  the  place  it 
would  have  reached  had  only  one  of  the  forces  acted  upon 
it,  as  it  would  have  been  had  it  been  at  rest  at  this  point, 
and  acted  upon  by  the  other  force  alone  for  the  same  time. 

For  example,  suppose  the  spring  would  send  the  ball  for- 
ward 30  feet  in  a  second,  and  the  force  of  gravity  pulls  it 
from  a  state  of  rest  16  feet  towards  the  earth  in  the  same 
time,  the  ball  at  the  end  of  the  second  will  be  just  16 
feet  below  the  point  it  would  have  reached  had  only  the 
force  of  the  spring  acted  upon  it.  So,  were  a  ball  thrown 
directly  upward  with  a  velocity  of  100  feet  a  second,  at 
the  end  of  the  second  it  would  be  only  84  feet  high,  that 
is,  1 6  feet  below  the  point  it  would  have  reached  had  not 
the  force  of  gravity  acted  upon  it.  If  it  were  thrown  di- 
rectly downward  from  the  top  of  a  high  tower  with  the 
same  velocity,  it  would  be  at  the  end  of  a  second  116 


52  NATURAL    PHILOSOPHY. 

feet  below  the  top  of  the  tower,  that  is,  16  feet  below 
the  point  it  would  have  reached  had  not  gravity  acted 
upon  it.  Now  1 6  feet  is  just  the  distance  in  each  of 
the  above  cases  that  gravity  would  have  pulled  the  ball 
in  a  second  from  a  state  of  rest. 

Again,  suppose  that  the  current  in  a  stream  is  strong 
enough  to  carry  a  boat  down  stream  one  mile  in  an 
hour,  and  a  person  attempts  to  row  the  boat  directly 
across  the  stream  at  a  rate  which  would  take  him  across 
in  an  hour,  at  the  end  of  the  hour  the  boat  would  be  at 
the  opposite  bank  just  a  mile  down  stream. 

57.  A  Body  thrown  horizontally  or  obliquely  when  acted 
upon  by  Gravity  describes  a  curved  Path.  —  When  both 
the  forces  acting  upon  the  body  are  instantaneous,  it 
moves  in  a  straight  line ;  when  one  is  instantaneous  and 
the  other  continuous,  as  in  the  case  of  gravity  acting  on 
a  ball  thrown  horizontally  or  obliquely,  the  path  is  curved. 
The  curved  path  described  by  a  body  when  acted  upon 
by  an  instantaneous  and  a  continuous  force  is  well  illus- 
trated by  a  jet  of  water  issuing  from  the  side  of  a  vessel. 
The  lateral  pressure  is  the  instantaneous  force  acting  upon 
each  particle  of  water  as  it  issues  from  the  opening  ;  and 
the  force  of  gravity  acting  upon  it  after  it  leaves  the  open- 
ing is  the  continuous  force.  The  curved  path  in  this 
case  is  called  a  parabola. 

On  account  of  this  effect  of  gravity  upon  a  body 
moving  horizontally  or  obliquely,  a  cannon-ball  describes 
a  curved  path.  If  then  a  cannon  or  a  musket  is  fired 
at  a  distant  object,  it  must  be  aimed  above  it. 

We  have  a  good  illustration  of  the  second  law  of  mo- 
tion in  the  case  of  falling  bodies. 


NATURAL    PHILOSOPHY. 


53 


FALLING  BODIES. 


Fig.  44- 


58.  All  Bodies   would  fall  at  the 
same  Rate,  were  it  not  for  the  Resist- 
ance of  the  Air.  —  As  we  see  bodies 
light   and  heavy  falling   through   the 
air,  we  come  to  think  that  the  force 
of  gravity  causes  heavy  bodies  to  fall 
more  rapidly  than  light  ones  ;  but  if 
we   place  a  coin  and  a  feather  in  a 
long  glass  tube  and  exhaust  the   air 
completely,    on    inverting    the     tube 
(Figure  44)   the  two  bodies  will  fall 
through  it  in  the  same  time.     It  must 
be  therefore  the  resistance  of  the  air 
which  causes   a  lighter   body  to   fall 
more  slowly  through  the  atmosphere 
than  a  heavy  one  does. 

When  therefore  the  force  of  gravity 
is  unimpeded  in  its  action,  it  will 
?ause  every  body,  whatever  may  be 
vts  size,  shape,  or  density,  to  fall  with 
exactly  the  same  speed. 

59.  When  a    Body    is    moving    di- 
rectly downward  Gravity  increases  its 

Velocity  at  the  Rate  0/32  Feet  a  Second.  —  It  is  found  by 
means  of  a  pendulum  that  a  body  falls  16  feet  the  first 
second,  and  acquires  a  velocity  of  32  feet  during  the 
time.  As  gravity  has  the  same  effect  upon  a  moving 
body  as  upon  one  at  rest,  a  falling  body  will  gain  in 
velocity  32  feet  each  second.  When  therefore  a  body 
is  moving  directly  downward,  gravity  increases  its  ve- 
locity at  the  rate  of  32  feet  a  second. 

60.  How  to  find  the  Distance  a  Body  falls  in  a  given 
Time.  —  As  we  have  seen,   a  body  when  falling  from  a 


54  NATURAL    PHILOSOPHY. 

state  of  rest  has  a  velocity  of  32  feet  at  the  end  of  the 
first  second,  and  falls  16  feet  during  that  second.  This 
distance  is  exactly  the  mean  between  o,  its  velocity  at 
starting,  and  32,  its  velocity  at  the  end  of  the  second. 
As  it  would  gain  a  velocity  of  32  feet  during  the  next 
second,  it  would  have  a  velocity  of  64  feet  at  the  end 
of  that  second.  The  velocity '  it  has  already  acquired 
would  cause  it  to  fall  32  feet  the  second  second,  and 
the  force  of  gravity  acting  upon  it  during  that  time 
would  cause  it  to  fall  16  feet  more  ;  hence  it  would  fall 
48  feet  during  the  second  second.  It  will  be  noticed 
that  48  is  just  the  mean  of  32,  its  velocity  at  the  begin- 
ning of  the  second,  and  64,  its  velocity  at  the  end  of  the 
second. 

During  the  first  two  seconds  the  body  would  fall  48  -f- 
16  =  64  feet.  This  is  just  twice  the  mean  of  o  and  64. 
Hence,  to  find  the  distance  that  any  body  would  fall 
when  acted  upon  by  gravity  alone  during  any  number 
of  seconds,  find  its  mean  velocity  during  the  time,  and 
multiply  it  by  the  number  of  seconds. 

To  find  the  velocity  of  a  falling  body  at  the  end  of 
any  second,  multiply  32  feet  by  the  number  of  seconds 
it  has  been  falling. 

6 1.  When  a  Body  is  moving  directly  upward  Gravity  re- 
tards its  Velocity  at  the  Rate  of  32  Feet  a  Second.  — We  have 
already  seen  that  gravity  has  the  same  effect  on  a  body  in 
motion  as  on  one  at  rest.     Since,  then,  it  causes  a  body  in 
falling  from  a  state  of  rest  to  acquire  a  velocity  of  32  feet  a 
second,  it  must,  in  the  case  of  a  body  moving  directly  up- 
ward, diminish  its  velocity  at  the  rate  of  32  feet  a  second. 
And  it  must  also  cause  it  to  rise  each  .second  16  feet  less 
than  if  it  were  not  acting  upon  it. 

62.  How  to  find  the  Distance  a  Body,  when  thrown  up- 
ward, will  rise  in  a  given  Time. — To  find  this  distance,  take 
the  mean  velocity  of  the  body  during  the  time,  and  multi- 


NATURAL    PHILOSOPHY.  '55 

ply  it  by  the  number  of  seconds.  To  find  the  velocity  at 
any  particular  second,  multiply  the  number  of  seconds  the 
body  has  been  rising  by  32,  and  subtract  this  from  the 
velocity  the  body  has  at  starting. 

63.  A  Body  always  acquires  the  same  Velocity  in  falling 
the  same  Distance.  —  It  has  been  found  that  a  body  in  roll- 
ing down  an  inclined  plane  (allowance  being  made  for  fric- 
tion) acquires  the  same  velocity  that  it  would  have  acquired 
in  falling  a  distance  equal  to  the  height  of  the  inclined 
plane.  So,  too,  in  the  case  of  a  pendulum-ball,  if  it  be 
drawn  up  to  the  point  C  (Figure  45),  f. 

and  then  allowed  to  fall  to  B,  it  will,  on 
reaching  B,  have  the  same  velocity  it 
would  have  had  in  falling  from  C  to  Z>. 
And  it  is  found  to  be  true  in  general, 
that  bodies  always  acquire  the  same 
velocity  in  falling  the  same  distance  J)1 — — 
from  a  state  of  rest,  no  matter  what 
path  they  may  take. 


PROBLEMS. 

SECOND   LAW   OF  MOTION. 

Gravity  causes  a  body  to  fall  from  a  state  of  rest 
4.9  metres  in  a  second,  and  increases  its  velocity  9.8 
metres  in  a  second. 

56.  A   body   falls   from  a  state   of  rest.      How  many 
metres  of  velocity  has  it  at  the  end  of  the  third  second  ? 

57.  A  body  is  thrown  downward  with  a  velocity  of  50 
metres  a  second.     What  will  be  its  velocity  at  the  end  of 
7  seconds? 

58.  A  body  is  thrown  downward  with  a  velocity  of  23 
metres  a  second.     What  will  be  its  velocity  at  the  end  of 
9  seconds  ? 


56  NATURAL    PHILOSOPHY. 

59.  A  body  is  thrown  upward  with  a  velocity  of  42 
metres  a  second.      What  will  be  its  velocity  at  the  end 
of  4  seconds  ? 

60.  A  body  is  thrown  upward  with  a  velocity  of  75 
metres  a  second.      What  will  be  its  velocity  at  the  end 
of  5  seconds  ? 

6 1.  A  body  is  thrown  upwarrl  with  a  velocity  of  98 
metres  a  second.     How  long  will  it  continue  to  rise  ? 

62.  How  high  will  the  above  body  rise  ? 

63.  How  far  will  it  rise  the  first  3  seconds  ? 

64.  How  far  will  it  rise  the  last  3  seconds  ? 

65.  How  far  will  it  rise  from  the  beginning  of  the  3d  to 
the  end  of  the  8th  second  ? 

66.  Two  bodies  are  thrown  upward,  one  with  a  velocity 
of  68.6  metres  a  second,  and  the  other  with  a  velocity  of 
137.2   metres  a  second.     How  many  seconds  will  it  be 
before  e^ch  begins  to  fall  ? 

67.  To  what  height  would  each  rise  ? 

68.  One  ball  is  thrown  upward  with  a  velocity  of  78.4 
metres  a  second,  and   another  with   twice   this  velocity. 
The  last  ball  will  rise  how  many  times  as  high  as  the  first  ? 

69.  If  the  second  ball  had  been  thrown   with   thrice 
the  velocity  of  the  first,  how  many  times  as  high  would  it 
have  risen  ? 

70.  If  it  had  been  thrown  with  four  times  the  velocity, 
how  many  times  as  high  would  it  have  risen  ? 

71.  A  ball  falls  from  a  state  of  rest,  and  reaches  the 
earth  in  12  seconds.     With  what  velocity  does  it  strike  the 
earth  ? 

72.  From  what  height  did  the  ball  in  the  last  example 
fall? 

73.  How  far  did  it  fall  the  first  5  seconds  ? 

74.  How  far  did  it  fall  the  last  5  seconds  ? 

75.  How  far  did  it  fall  from  the  beginning  of  the  3d  to 
the  end  of  the  5th  second? 


NATURAL   PHILOSOPHY.  57 

76.  How  far  did  it  fall  from  the  beginning  of  the  8th 
to  the  end  of  the  nth  second? 

77.  A  ball  is  thrown  downward  with  a  velocity  of  125 
metres  a  second,  and  reaches  the  earth  at  the  end  of  7 
seconds.     What  is  its  velocity  on  reaching  the  earth  ? 

78.  From  what  height  was  the  ball  in  the  last  example 
thrown  ? 

79.  Through  what  distance  did  it  pass  from  the  begin- 
ning of  the  3d  to  the  end  of  the  6th  second  ? 

80.  A  stone  falls  from  a  state  of  rest,  and  is  4  seconds 
in  reaching  the  earth.     With  what  velocity  does  it  strike 
the  earth  ?     Through  what  distance  does  it  fall  ? 

8 1.  If  the  stone  had  reached  the  earth  in  8  seconds, 
what  velocity  would  it  have  acquired,  and  through  what 
distance  would  it  have  fallen  ? 

82.  If  the  stone  had  reached  the  earth  at  the  end  of  12 
seconds,  with  what  velocity  would  it  have   reached    the 
earth,  and  through  what  distance  would  it  have  fallen?* 

83.  A  body  in   falling    from   a   state   of  rest   through 
4.9   metres  acquires  a  velocity  of  9.8   metres  a  second. 
Through  what  distance  must  it  fall  in  order  to  double 
this  velocity? 

84.  Through   what   distance   must   it   fall  in   order  to 
treble  this  velocity  ? 

85.  A  stone  falls  from  a  height  of  19.6  metres.     With 
what  velocity  does  it  reach  the  earth  ? 

NOTE.  —  We  see  from  problems  80  -  85  that  the  velocity 
of  a  body  increases  as  the  square  root  of  the  distance  through 
which  it  falls  from  a  state  of  rest.  We  see  from  problems 
66-70  that  the  height  to  which  a  body  will  rise  increases 
as  the  square  of  the  velocity  with  ivhich  it  starts. 

*  See  Appendix,  II. 
3* 


58  NATURAL   PHILOSOPHY. 

THIRD   LAW   OF  MOTION. 

64.  Momentum.  —  If  balls  of  lead  of  different  size  be 
placed  in  the  cavity  of  the  arm  CD  (Figure  43),  and  the 
arm  be  drawn  back  to  exactly  the  same  point  each  time, 
the  balls  will  not  all  be  thrown  to  the  same  distance.  The 
smaller  the  ball  the  farther  it  will  be  thrown.  If  one 
ball  is  twice  as  heavy  as  another,  it  will  be  thrown  only 
one  half  as  far ;  if  three  times  as  heavy,  only  one  third 
as  far ;  and  so  on. 

The  same  is  true  when  the  balls  are  of  different  materi- 
als, provided  their  mass  is  different  By  the  mass  of  a 
body  we  mean  its  quantity  of  matter.  This  is  usually 
measured  by  its  weight ;  that  is,  if  a  body  weighs  twice  as 
much  as  another,  its  mass  is  said  to  be  double ;  if  thrice 
as  much,  its  mass  is  said  to  be  treble ;  and  so  on. 

We  see  then  that  the  same  force  acting  upon  bodies  con- 
taining different  quantities  of  matter  does  not  impart  to 
each  the  same  velocity;  and  that  the  force  acting  upon 
each  being  the  same,  the  velocity  will  be  in  the  inverse 
ratio  of  the  quantities  of  matter  that  they  contain ;  that  is, 
if  the  quantity  of  matter  in  each  be  multiplied  by  its  ve- 
locity, the  products  will  all  be  equal. 

The  product  of  the  velocity  of  a  body  multiplied  by  its 
mass  is  called  its  momentum. 

The  same  force,  then,  will  impart  the  same  momentum 
Fig.  46.  t°  a  body,  whether  that  body  be  large 

or  small. 

65.  A  moving  Body  cannot  impart 
Motion  to  another  Body  without  itself 
losing  the  same  Quantity  of  Motion.  — 
Hang  two  balls  of  lead  or  clay  side  by 
side,  as  shown  in  Figure  46,  and  place 
behind  them  an  arc  graduated  so  that 
the  line  2  b  shall  be  four  times  as 


NATURAL    PHILOSOPHY.  59 

long  as  i  a ;  3  <r,  9  times  as  long  as  i  a  ;  and  4  */,  16  times 
as  long  as  i  a. 

Now,  if  one  of  the  balls  be  drawn  back  to  the  division 
2  on  the  scale,  and  dropped,  it  will,  as  we  have  seen, 
(note,  page  57,)  on  reaching  the  other  ball,  acquire  twice 
the  velocity  it  would  have  acquired  had  it  been  dropped 
from  division  i  ;  and  if  dropped  from  division  3,  it  will 
acquire  three  times  the  velocity  it  would  have  acquired 
had  it  been  dropped  from  i. 

If  now  both  balls  are  of  the  same  weight,  and  one  of 
them  be  raised  to  the  division  2  and  dropped,  on  striking 
the  other  ball  it  will  move  on  with  that  ball  to  i.  The 
momentum  of  the  first  ball  is  then  sufficient  to  cause  both 
balls  to  move  on  to  this  division.  Now,  to  cause  the  balls 
to  rise  to  this  division,  they  must  start  with  just  half  the 
velocity  that  the  first  ball  had  on  reaching  the  second  ball. 
The  momentum  of  the  balls  after  collision  is  then  the  same 
as  that  of  the  moving  ball  before  collision.  The  moving 
ball  has  then  imparted  to  the  ball  at  rest  a  quantity  of 
motion  equal  to  half  its  own,  and  has  in  turn  lost  half 
its  own  motion. 

Put  now  in  the  place  of  these  balls  two  other  balls  of 
unequal  size,  whose  joint  weight  shall  be  equal  to  that  of 
the  first  balls,  and  let  the  weight  of  the  smaller  ball  be  just 
one  third  that  of  the  larger  ball.  If  now  this  ball  be  raised 
to  4  and  dropped,  it  will  acquire  on  reaching  the  larger  ball 
twice  the  velocity  of  the  ball  first  dropped  from  2  ;  and  as 
its  mass  is  just  half  the  mass  of  that  ball,  its  momentum 
will  be  the  same.  On  allowing  it  to  fall  from  4  against  the 
larger  ball,  the  two  will  move  on  together  to  i.  But  this 
is  just  the  height  to  which  the  balls  moved  in  the  first  ex- 
periment. The  balls,  then,  after  collision,  have  the  same 
momentum  that  the  moving  ball  had  before  collision. 
Since,  after  collision,  the  balls  have  one  fourth  the  velocity 
of  the  smaller  ball  before  collision,  the  smaller  ball  will 


60  NATURAL    PHILOSOPHY. 

have  only  one  fourth  the  motion  it  had  before,  while  the 
larger  ball  will  have  three  times  the  motion  of  the  smaller 
one,  or  three  fourths  the  motion  the  smaller  one  had  before 
collision.  The  smaller  ball  has  then  imparted  to  the  larger 
one  a  quantity  of  motion  equal  to  three  fourths  its  own, 
and  has  in  turn  lost  three  fourths  its  own  motion. 

If  two  equal  balls  of  ivory,  or  some  other  very  elastic 
substance,  are  hung  side  by  side,  and  one  of  them  is  raised 
and  dropped  against  the  other,  on  collision  the  first  ball 
comes  to  rest,  and  the  second  ball  starts  off  with  a  velocity 
equal  to  that  which  the  first  had  acquired. 

It  is  found  to  be  true  in  every  case  that  a  moving  body 
cannot  impart  motion  to  another  body  without  itself  losing 
the  same  quantity  of  motion.  This  is  usually  called  the 
law  of  action  and  reaction,  and  stated  thus  :  action  and  reac- 
tion are  always  equal  and  in  opposite  directions. 

This  law  is  the  result  of  the  inability  of  a  moving  body 
of  itself  either  to  increase  or  to  lessen  its  quantity  of  motion. 
On  meeting  another  body  it  may  impart  some  of  its  own 
motion  to  it ;  but  it  cannot  give  motion  to  this  body,  and 
at  the  same  time  retain  all  its  own  motion. 

66.  Other  Cases  of  Action  and  Reaction. — When  any  force 
acts  in  opposite  directions,  it  is  usually  said  to  act  in  one  di- 
rection, and  react  in  the  opposite.  Thus  in  firing  a  cannon, 
the  expansive  force  of  the  gases  suddenly  set  free  by  the 
burning  powder  acts  equally  in  all  directions.  It  acts 
upon  the  sides  with  equal  and  opposite  forces  which  neu- 
tralize each  other  unless  the  cannon  bursts.  It  also  acts 
toward  the  muzzle  and  breech  with  equal  forces,  which 
produce  equal  effects,  one  upon  the  ball  and  the  other  on 
the  cannon,  causing  the  recoil.  The  ball  and  the  cannon 
both  have  the  same  momentum,  but  the  ball,  since  it  has  a 
much  less  mass,  gets  a  much  greater  velocity.  This  expan- 
sive force  is  said  to  act  upon  the  ball  and  to  react  upon  the 
gun.  So,  toor  in  walking,  we  are  sajd  to  react  upon  the 


NATURAL    PHILOSOPHY.  6 1 

earth,  The  truth  is,  that  the  bent  leg  acts  like  a  bent 
spring  between  our  bodies  and  the  earth,  and  when  the 
spring  straightens  it  pushes  us  away  from  the  earth  and 
the  earth  away  from  us  ;  the  earth  being  moved  as  much 
less  than  our  bodies  as  its  mass  is  greater. 

67.  It  requires  Time  to  impart  Motion  to  a  Body  as  a 
Whole.  —  The  forces  which  impart  motion  to  a  body  often 
act  directly  upon  only  a  few  of  its  particles.  When  a  ball 
is  struck  by  a  bat,  only  a  small  part  of  it  receives  the  blow, 
and  when  a  bullet  is  shot  from  a  gun,  the  gases  (46)  act 
only  upon  one  half  of  it.  When  a  body  is  thus  set  in  mo- 
tion by  a  force  acting  upon  only  a  few  of  its  particles,  it  is 
clear  that  the  motion  must  be  transmitted  from  particle  to 
particle.  Now,  this  transmission  of  motion  from  particle 
to  particle  requires  time,  although  this  time  may  be  exceed- 
ingly short.  If  the  force  acts  so  suddenly  that  there  is  not 
time  enough  for  this  transmission,  the  part  acted  upon  is 
flattened  or  chipped  off.  Thus  a  musket  ball  may  be  fired 
through  a  window  pane,  making  a  clear  round  hole  without 
cracking  the  glass.  If  the  ball  had  been  thrown  by  the 
hand,  the  whole  pane  would  have  been  shattered.  In  the 
first  case  the  speed  of  the  ball  was  so  great  that  the  par- 
ticles in  front  of  it  had  not  time  to  transmit  their  motion 
to  those  about  them  \  hence  they  moved  on  alone,  leaving 
the  others  at  rest.  If  the  pane  had  been  suspended  by  a 
fine  thread,  the  ball  would  have  passed  through  it  in  the 
same  way,  without  breaking  the  thread,  or  causing  the 
pane  to  swing  in  the  least.  So  a  door  half  open  may  be 
pierced  by  a  cannon-ball  without  being  shut.  The  end  of 
a  musket  in  a  soldier's  hand  has  been  known  to  be  carried 
away  by  a  cannon-ball  without  his  being  aware  of  it.  It  is 
a  well-known  fact  that  a  tallow-candle  may  be  fired  through 
a  board,  since  it  gets  through  it  before  the  parts  of  the  tai- 
low  have  time  to  yield.  In  this  way  a  soft  missile  may  hit 
as  hard  as  lead  if  fired  with  sufficient  speed. 


62  NATURAL    PHILOSOPHY. 

We  see,  then,  that  when  a  moving  body  meets  with  an- 
other it  seldom  expends  all  its  power  in  imparting  motion 
to  that  body  as  a  whole,  but  also  pierces  it  more  or  less. 
The  power  of  a  body  to  pierce  another  increases  as  the 
square  root  of  its  velocity ;  that  is,  if  a  body  is  to  pierce 
another  twice  as  far,  it  must  have  four  times  the  velocity  j 
if  three  times  as  far,  nine  times  the  velocity  ;  and  so  on. 

68.  Reflected  Motion.  —  When  an  elastic  ball  is  thrown 
against  the  floor  it  rebounds.  If  it  is  thrown  directly 
downward,  it  retraces  its  path  in  its  rebound.  If  it  is 
thrown  obliquely,  it  rebounds  obliquely  in  an  opposite 
direction.  In  Figure  47,  if  the  ball  is  thrown  in  the  direc- 
tion af,  it  will  rebound  in  the  di- 
rection /  b.  If  the  line  e  f  be 
drawn  at  right  angles  to  the  sur- 
face, the  angle  formed  by  the  two 

j     lines   af  and    ef  is    called    the 

f  angle   of  incidence,   and  is   always 

equal  to  the  angle  formed  by  the  two  lines  b  f  and  e  f. 
This  last  angle  is  called  the  angle  of  reflection.  In  reflected 
motion  the  angle  of  incidence  always  equals  the  angle  of  re- 
flection. 

SUMMARY. 

A  moving  body,  when  left  to  itself,  will  always  move  in  a 
straight  line  and  at  the  same  rate.  (50.) 

An  unbalanced  force  must  act  upon  a  body  in  order  to 
put  it  in  motion,  or  to  change  the  direction  or  rate  of  its 
motion.  (51.) 

When  a  force  acts  upon  a  body  for  a  moment  only,  the 
motion  which  it  gives  it  is  gradually  wasted  away,  owing 
to  the  resistance  which  the  body  meets.  (52.) 

The  resistance  which  a  moving  body  meets  increases  as 
the  square  of  the  velocity  of  its  motion.  (54.) 


NATURAL    PHILOSOPHY.  63 

A  body  moving  in  a  straight  line  and  with  uniform  ve- 
locity is  in  equilibrium.  (55.) 

An  unbalanced  force  has  the  same  effect,  whether  it  act 
upon  a  body  at  rest  or  in  motion,  and  whether  it  act  alone  or 
with  other  forces.  (56.) 

A  body  thrown  horizontally  or  obliquely,  when  acted 
upon  by  gravity,  is  made  to  move  in  a  curved  path.  (57.) 

Were  it  not  for  the  air,  a  light  body  would  fall  as  fast  as 
a  heavy  one.  (58.) 

Gravity  acting  alone  causes  a  body  to  fall  from  a  state 
of  rest  about  16  feet  in  a  second. 

When  a  body  is  moving  directly  downward  gravity  in- 
creases its  velocity  at  the  rate  of  32  feet  a  second.  (59.) 

When  a  body  is  moving  directly  upward  gravity  retards 
its  velocity  at  the  rate  of  32  feet  a  second.  (61.) 

The  velocity  of  a  body  increases  as  the  square  root  of 
the  space  through  which  it  falls. 

The  height  to  which  a  body  will  rise  increases  as  the 
square  of  the  velocity  with  which  it  starts.  (Note,  page  57.) 

A  body  always  gains  the  same  velocity  in  falling  from 
the  same  height,  whether  it  falls  directly  downward  or 
obliquely.  (63.) 

The  same  force  always  gives  to  a  body  the  same  quan- 
tity of  motion. 

The  quantity  of  a  body's  motion  is  found  by  multiplying 
its  weight  by  its  velocity.  (64.) 

A  moving  body  cannot  impart  motion  to  another  body  with- 
out itself  losing  the  same  quantity  of  motion.  (65.) 

When  the  same  force  acts  in  opposite  directions,  it  is 
usually  said  to  act  in  one  direction  and  to  react  in  the  op- 
posite. (66.) 

It  requires  time  to  give  motion  to  a  body  as  a  whole. 

(67.) 

In  reflected  motion  the  angle  of  incidence  equals  the 
angle  of  reflection.  (68.) 


64  NATURAL    PHILOSOPHY. 

PROBLEMS. 

THIRD   LAW   OF  MOTION. 

^§f*  To   find   the   momentum   of  a  body,  multiply  its 
weight  in  grammes  by  its  velocity  in  metres. 

86.  A  body  weighs  50  kilogrammes  and  is  moving  at 
the  rate  of  1 2  metres  a  second.     What  is  its  momentum  ? 

87.  The  same  body  is  moving  at  the  rate  of  5  metres  a 
second.     What  is  its  momentum  ? 

88.  With  what  velocity  must  a  body  weighing  6  grammes 
move,  in  order  to  have  the  same  momentum  as  a  body 
weighing  500  kilogrammes   and  moving  at  the  rate  of  2 
metres  a  second  ? 

89.  A  certain  force  gives  to  a  body  weighing  45  kilo- 
grammes  a  velocity  of  9   metres   a  second.      What  ve- 
locity would  the  same  force  give  to  a  body  weighing  3 
grammes  ? 

90.  A  body  weighing  5  kilogrammes  and  moving  at  the 
rate  of  175  metres  a  second  meets  a  body  at  rest  weighing 
85  kilogrammes,  and  after  meeting  they  both  move  on  to- 
gether.    What  is  their  velocity  ? 

91.  What  is  the  momentum  of  the  larger  body? 

92.  What  is  the  momentum  of  the  smaller  body,  and 
how  much  momentum  has  it  lost  ? 

93.  If  the  larger  body  had  weighed   20  kilogrammes, 
what  would  have  been  their  velocity  after  meeting,  and 
how  much  momentum  would  the  smaller  body  have  lost  ? 

94.  If  the  second  body  had  weighed  3  grammes,  what 
would  have  been  the  velocity  of  the  bodies  after  meeting, 
and  how  much  momentum  would  the  first  body  have  lost  ? 


NATURAL    PHILOSOPHY. 


THE   PENDULUM. 

75.  A  pendulum  is  a  heavy  body  hung  from  a  fixed  point 
by  means  of  a  cord  or  rod.     When  the  centre  of  gravity  of 
the  body  is  directly  under  the  point  of  support,  the  body 
remains  at  rest ;  but  if  the  body  be  drawn  out  of  this  posi- 
tion, it  will  on  being  let  go  fall  towards  a  vertical  line  pass- 
ing through  the  point  of  support,  and  when  it  has  reached 
this  line  it  will,  owing  to  its  inertia,  pass  beyond  it.     On 
coming  to  rest  it  again  falls  toward  this  vertical  line  and 
again  passes  beyond,  and  thus  continues  to  swing  from 
side  to  side. 

There  are  two  kinds  of  pendulum,  the  simple  pendulum 
and  the  compound  pendulum. 

76.  The  Simple  Pendulum.  — A  simple  pendulum  consists 
of  a  material  point,  suspended  to  a  fixed  point  by  means 
of  a  thread  without  weight,  perfectly  flexible,  and  incapable 
of  stretching.     Such  a  pendulum  has  of  course   no  real 
existence  ;  but  we  can  approach  suffi- 
ciently near  to  it,  for  purposes  of  illus- 
tration,  by   suspending   a    small    lead 

bullet  to  a  fixed  point  by  means  of  a 
fine  silk  thread. 

77.  First  Law  of  the  Vibration  of  the 
Pendulum.  —  Suppose  d,  in  Figure  48, 
to  be  a  leaden  ball  hanging  by  a  fine 
silk  thread.     Pull  it  to  one  side  so  that 
it  shall  swing  through  an  arc  of  some 
3°,  and  count  the  number  of  its  vibra- 
tions in  a  minute.    Now  bring  it  to  rest 
again,  and  draw  it  to  one  side  so  that 
it  shall  swing  through  an  arc  of  2°,  and 
again  count  its  vibrations  in  a  minute. 
Again  bring  the  ball  to  rest,  then  cause 


Fig.  48. 


66  NATURAL    PHILOSOPHY. 

it  to  swing  through  an  arc  of  i°,  and  count  the  vibrations 
in  a  minute.  In  all  three  cases  the  number  of  vibrations 
in  a  minute  will  be  equal. 

By  a  vibration  is  meant  the  whole  of  the  pendulum's 
movement  in  one  direction.  The  arc  through  which  the 
pendulum  swings  is  called  the  amplitude  of  its  vibration. 

The  above  experiment  shows  that,  when  the  length  of  the. 
pendulum  remains  the  same,  and  the  amplitude  of  the  vibra- 
tion does  not  exceed  3°,  the  pendulum  always  vibrates  in  the, 
same  time,  whatever  be  the  amplitude  of  the  vibration. 

This  singular  property  of  the  pendulum  is  called  isoch- 
ronism,  from  two  Greek  words  signifying  equal  times,  and 
the  vibrations  of  the  pendulum  are  said  to  be  isochronous. 

78.  The  Second  Law  of  the  Vibration  of  the  Pendulum.  — 
Let  d  and  c  in  figure  48  be  two  pendulums  exactly  alike, 
except  that  the  ball  of  one  is  lead,  and  of  the  other  ivory. 
Let  each  swing  through  a  small  arc,  and  count  its  vibrations 
in  a  minute.     It  will  be  found  that,  making  allowance  for 
the  resistance  of  the  air,  each  performs  the  same  number 
of  vibrations  in  the  same  time.     This  gives  the  second  law 
of  the  vibration  of  the  pendulum,  namely  :  for  pendulums 
of  the  same  length,  the  time  of  the  vibration  is  the  same,  what- 
ever the  pendulum  may  be  made  of. 

79.  Third  Law  of  the  Vibration  of  the  Pendulum.  —  Let 
b  in  Figure  48  be  a  pendulum  one  fourth  the  length  of  c, 
and  a  another,  one  ninth  the  length  of  c.     Set  each  swing- 
ing through  a  small  arc,  and  count  the  vibrations  of  each 
in  a  minute.     It  will  be  found  that  b  vibrates  twice  as  fast 
as  c,  and  a  three  times  as  fast  as  c.     This  shows  that,/*??- 
Pendulums  of  unequal  length,  the  time  of  the  vibration  is  pro- 
portional to  the  square  root  of  the  length;  that  is,  the  lengths 
of  the  pendulum  being  made  4,  9,  and  16  times  greater, 
the  time  of  the  vibration  of  the  pendulum  will  be  only  2,  3, 
and  4  times  longer.     This  is  the  third  law  of  the  vibration 
of  the  pendulum. 


NATURAL   PHILOSOPHY.  67 

80.  Fourth  Law  of  the  Vibration  of  the  Pendulum.  —  It 
is  found  that  when  a  pendulum  of  a  given  length  is  placed 
on  different  parts  of  the  earth's  surface,  the  time  of  the 
vibrations  is  not  always  the  same.     Towards  the  poles  it  is 
found  to  vibrate  more  rapidly  than  at  the  equator.    Mathe- 
maticians have  shown  that  this  is  because  the  force  of 
gravity  is  stronger  at  the  poles.     They  have  shown  that, 
in  different  parts  of  the  earth,  the  time  of  the  vibration  for 
pendulums  of  the  same  length  is  in  the  inverse  ratio  of  the 
square  root  of  the  intensity  of  gravity.     That  is,  if  the  inten- 
sity of  gravity  were  four  times  as  great  in  one  place  as  in 
another,  the  time  of  the  vibration  of  a  pendulum  of  the 
same  length  would  be  half  as  great,  and  so  on. 

8 1.  The  Compound  Pendulum. — The  simple  pendulum, 
as  has  been  stated,  can  have  no  real  existence.      Every 
pendulum  actually  used  is  a  compound  pendulum,  consist- 
ing of  a  heavy  weight  hung  from  a  fixed  point  by  means  of 
a  rod  of  wood  or  metal.    The  particles  of  such  a  pendulum 
must  of  course  be  at  different  distances  from  the  point  of 
suspension,  and  must  therefore  tend  to  vibrate  in  different 
times.    Hence  the  time  of  vibration  of  the  whole  pendulum 
will  not  be  the  same  as  that  of  a  simple  pendulum  of  the 
same  length. 

The  compound  pendulum  may  be  regarded  as  consisting 
of  as  many  simple  pendulums  as  it  contains  particles.  If 
these  were  free  to  move,  they  would  vibrate  in  times  de> 
pending  upon  their  distances  from  the  point  of  suspension  • 
but  since  they  are  united  in  one  body,  they  are  all  com- 
pelled to  vibrate  in  the  same  time.  Consequently,  the 
vibrations  of  the  particles  near  the  point  of  suspension  are 
retarded  by  the  slower  vibrations  of  the  particles  below 
them ;  and,  on  the  other  hand,  the  vibrations  of  the  par- 
tides  near  the  lower  end  of  the  pendulum  are  quickened 
by  the  more  rapid  vibrations  of  those  above  them.  At 
some  point  between  these  there  must  be  a  particle  whose 


68  NATURAL    PHILOSOPHY. 

vibration  is  neither  retarded  nor  quickened,  —  all  the  par- 
ticles above  having  just  the  same  tendency  to  vibrate  faster 
that  those  below  have  to  vibrate  slower.  This  point  is 
called  the  centre  of  vibration,  and  it  is  obvious  that  the  time 
of  vibration  of  a  compound  pendulum  is  the  same  as  that 
of  a  simple  pendulum  whose  length  is  equal  to  the  dis- 
tance of  the  centre  of  vibration  from  the  point  of  sus- 
pension. This  distance  is  the  virtual  length  of  the  pen- 
dulum. 

When  the  form  of  the  pendulum  is  given,  the  position 
of  the  centre  of  vibration  can  be  found  experimentally  by 
making  use  of  a  remarkable  property  of  the  compound 
pendulum,  namely,  that  if  such  a  pendulum  be  inverted 
and  suspended  by  its  centre  of  vibration,  its  former  point 
of  suspension  will  become  its  new  centre  of  vibration,  and 
the  time  of  vibration  will  be  the  same  as  before.  This 
property  is  usually  expressed  by  saying  that  the  centres  of 
vibration  and  suspension  are  interchangeable. 

To  find  the  centre  of  vibration,  then,  we  have  only  to 
reverse  a  pendulum,  and  by  trial  find  the  point  at  which  it 
must  be  suspended  in  order  to  vibrate  in  the  same  time  as 
it  did  before  it  was  reversed.  A  pendulum  constructed  for 
this  purpose  is  called  a  reversible  pendulum. 

82.  The  Use  of  the  Pendulum  for  Measuring  Time.  — 
The  most  important  use  of  the  pendulum  is  for  measuring 
time.  The  common  clock  is  merely  a  contrivance  for  re- 
cording the  beats  of  the  pendulum,  and  keeping  up  its 
motion.  The  essential  parts  of  such  a  clock  are  shown  in 
Figure  49.  The  toothed  wheel  R,  called  the  scape-wheel, 
is  turned  by  a  weight  or  spring,  and  its  motion  is  regulated 
by  the  escapement  n  m,  which  swings  on  the  axis  o;  the 
vibrations  of  the  pendulum  being  communicated  to  it  by 
means  of  the  forked  arm  a  b.  When  the  pendulum  is  at 
rest,  one  of  the  teeth  of  the  scape-wheel  rests  upon  the 
upper  side  of  the  hook  m,  and  the  clock  does  not  go.  If 


NATURAL   PHILOSOPHY. 


69 


now  the  pendulum  be  set  in  motion,  Fig.  49. 

so  that  the  hook  m  is  moved  from  the 
wheel,  the  tooth  which  rested  on  it  is 
set  free,  and  the  wheel  begins  to  turn ; 
but  it  is  soon  stopped  by  the  hook  /z, 
which  moves  up  to  the  wheel  as  m 
moves  away  from  it,  and  catches  on  its 
under  side  the  tooth  next  below.  As 
the  pendulum  swings  back,  the  hook  n 
moves  away,  the  wheel  again  begins  to 
turn,  but  is  stopped  again  on  the  oppo- 
site side  by  the  hook  m,  which  catches 
the  tooth  next  to  the  one  it  held  be- 
fore ;  and  thus  each  vibration  of  the 
pendulum  allows  the  scape-wheel  to 
move  forward  through  a  space  equal 
to  one  half  of  one  of  its  teeth.  If 
then  the  wheel  has  thirty  teeth,  it 
will  turn  around  once  in  sixty*  beats 
of  the  pendulum.  Upon  the  axis  of 
this  wheel  the  second-hand  of  the 
clock  is  placed.  It  is  connected  by 
cogs  with  another  wheel,  which  takes  sixty  times  as  long 
to  revolve,  and  which  carries  the  minute  hand ;  and  this 
latter  wheel  is  connected  with  another,  which  turns  in 
twelve  times  the  period,  and  carries  the  hour-hand.  Thus 
the  second-hand  registers  the  beats  of  the  pendulum  up 
to  sixty,  or  one  minute ;  the  minute-hand  registers  the 
revolutions  of  the  second-hand  up  to  sixty,  or  one  hour ; 
and  the  hour-hand  registers  the  revolutions  of  the  minute- 
hand  up  to  twelve,  or  half  a  day. 

Were  it  not  for  the  pendulum  and  escapement,  these 
wheels  would  be  whirled  round  very  fast  by  the  action 
of  the  weight  or  spring,  and  the  clock  would  soon  run 
down.  On  the  other  hand,  were  there  not  some  means 


70  NATURAL    PHILOSOPHY. 

of  keeping  up  the  motion  of  the  pendulum,  it  would 
soon  be  brought  to  rest  by  the  resistance  of  the  air 
and  the  friction  at  the  point  of  suspension.  Its  motion 
is  kept  up  by  means  of  the  escapement,  which  is  so  con- 
structed as  to  give  it  a  slight  push  at  each  vibration. 
The  ends  of  the  two  hooks  have  inclined  surfaces  against 
which  each  tooth  of  the  wheel,  as  it  leaves  them,  presses 
with  considerable  force,  so  as  to  throw  the  escapement  for- 
ward a  little  the  moment  the  tooth  is  set  free.  The  impulse 
thus  given  is  communicated,  through  the  axis  0,  and  the 
arm  a  b,  to  the  pendulum. 

83.  The  Use  of  the  Pendulum  for  measuring  the  Force  of 
Gravity.  —  We  have  seen  that  the  rate  of  the  vibration  of 
pendulums  of  the  same  length  depends  on  the  force  of 
gravity.  If  we  represent  by  g  the  velocity  that  a  body  fall- 
ing from  a  state  of  rest  would  acquire  during  a  second,  and 
by  /  the  length  of  a  pendulum  beating  seconds,  then  g  will 
be  equal  to  the  length  of  the  pendulum  multiplied  by  the 
square  of  the  number  3.1^16.  To  find  g,  we  have  only  to 
measure  the  length  of  a  pendulum  beating  seconds,  and 
then  to  multiply  this  length  by  the  square  of  the  number 
3.1416. 

Now  it  has  been  found  that  a  pendulum  beating  seconds 
at  London  must  be  39.13929  inches  long.  From  this  we 
get  £-=386  inches.  One  half  of  386  inches  is  193  inches, 
or  1 6  feet,  i  inch.  This  is  the  distance  which  a  body  will 
fall  from  a  state  of  rest  in  a  second. 

SUMMARY. 

A  pendulum  is  a  heavy  body  hung  from  a  fixed  point  by 
means  of  a  cord  or  rod.  (75.) 

The  laws  of  the  vibration  of  the  pendulum  are  best  in- 
vestigated by  means  of  a  simple  pendulum.  (76.) 

These  laws  are  four  in  number. 


NATURAL    PHILOSOPHY.  71 

i  st.  When  the  length  of  the  pendulum  remains  the  same, 
and  the  amplitude  of  the  yibrations  does  not  exceed  3°,  the 
pendulum  always  vibratts  in  the  same  time.  (77.) 

2d.  For  pendulums  of  the  same  length,  the  time  of  the 
vibrations  is  the  same,  whatever  the  pendulum  may  be 
made  of.  (78.) 

3d.  For  pendulums  of  different  lengths,  at  the  same  place, 
the  time  of  the  vibrations  is  proportional  to  the  square  root  of 
the  lengths.  (79.) 

4th.  In  different  parts  of  the  earth,  the  time  of  the  vibrations 
for  pendulums  of  the  same  length,  is  in  the  inverse  ratio  of 
the  square  root  of  the  intensity  of  gravity.  (80.) 

The  pendulum  in  ordinary  use  is  a  compound  pendulum. 
(81.) 

The  pendulum  is  used  for  measuring  time.     (82.) 

It  is  also  used  for  measuring  the  force  of  gravity.    (83.) 


PROBLEMS. 

95.  If  a  pendulum  beating  seconds  at  Paris  is  .99394  of 
a  metre  long,  what  would  be  the  length  of  one  beating 
half-seconds  ?     Of  one  vibrating  in  two  seconds  ? 

96.  If  a  pendulum  a-t  Paris  one  metre  long  vibrates  in 
1.00304  seconds,  what  will  be  the  time  of  vibration  for  a 
pendulum  9  metres  long?    What  for  one  25  metres  long? 
What  for  one  £  of  a  metre  long  ?    What  for  one  2\  metres 
long? 


NATURAL    PHILOSOPHY.  73 


III. 

MACHINES   AND    SOURCES    OF    MECHANICAL 
POWER. 

THE    LEVER. 

84.  When  a  workman  wishes  to  raise  a  large  stone,  he 
places  an  iron  bar  under  it,  as  in  Figure  50,  with  a  block 
under  the  bar  near  the    stone,  and 

then  presses   down    upon  the  other  Fig.  50. 

end  of  the  bar ;  or  else  he  places  the 
end  of  the  bar  under  the  stone,  as  in 
Figure  51,  so  that  one  end  of  it  rests 
upon  the  ground,  and  then  lifts 

upon  the  other  end.  The  iron  bar  thus  used  constitutes 
one  of  the  simple  machines.  It  is  called  the  lever.  The 
stone  to  be  raised  is  called  the  weight.  The  moving  force 
applied  at  the  other  end  of  the  bar  is  called  the  power; 
Fig.  51.  and  the  point  on  which  the  bar  rests 

is  called  the  fulcrum.  The  parts 
between  the  fulcrum  and  the  points 
where  the  power  and  weight  act  are 
the  arms  of  the  lever.  In  the  first 
case,  the  fulcrum  was  between  the  weight  and  the  power  : 
in  the  second  case,  the  weight  was  between  the  fulcrum  and 
the  power.  In  the  fishing  rod  (Figure  52)  one  hand  is  the 
fulcrum,  the  other  hand,  P,  is  the  Fi  52 

power,  and  the  fish  is  the  weight.     "1^^^-^^     f 
Here  the  power  is  applied  between      i 
the  fulcrum  and  the  weight. 

85.  Three  kinds  of  Lever.  —  We  see  from  the  above  that 
there  are  three  kinds  of  lever  :  — 

(i.)    That   with   the   fulcrum   between    the  weight   and 
power. 


74  NATURAL    PHILOSOPHY. 

(2.)  That  with  the  weight  between  the  fulcrum  and 
power. 

(3.)  That  with  the  power  between  the  fulcrum  and  the 
weight. 

These  three  kinds  of  lever  are  shown  in  Figure  53. 

Fig.  53- 


86.  The  Law  of  the  Lever.— IK  the  lever  of  the  first 
kind,  if  the  fulcrum  is  just  half  way  between  the  weight 
and  power,  then  on  moving  the  lever  a  little  the  weight 
and  power  will  move  through  equal  distances.  In  this  case 
it  is  found  that  the  weight  and  power  must  be  equal  in 
order  to  balance  each  other,  or  to  be  in  equilibrium.  If 
the  power  were  twice  as  far  from  the  fulcrum  as  the  weight, 
then  the  weight  would  move  through  only  half  the  distance 
that  the  power  does,  and  in  this  case  the  power  need  be 
only  half  the  weight  in  order  to  balance  it. 

Thus  we  see  that,  in  the  case  of  the  lever,  the  weight 
and  power  will  balance  each  other  when  the  power,  multi- 
plied by  the  distance  through  which  it  moves,  equals  the 
weight  multiplied  by  the  distance  through  which  it  moves. 
That  is,  if  the  fulcrum  of  a  lever  were  so  placed  that  one 
end  of  the  lever  would  move  through  a  thousand  inches 
while  the  other  end  moved  through  one  inch,  then  a  power 
of  one  pound  on  the  former  would  balance  a  weight  of  one 
thousand  pounds  on  the  latter. 


NATURAL    PHILOSOPHY.  75 

87.  The  Law  of  Machines  in   General. — The  same  is 
found  to  be  true  in  the  case  of  every  machine,  however 
complicated ;    namely,    that   the   power   and   weight   will 
balance  each  other  when,  on  setting  the  machine  in  mo- 
tion, the  power  multiplied  by  the  distance  through  which 
it  moves   equals   the  weight   multiplied   by  the  distance 
through  which  it  moves. 

There  is  no  real  gain  of  mechanical  force  in  a  lever  or  a 
machine  of  any  kind.  A  machine  is  only  an  arrangement 
by  which  a  small  force  acting  through  a  great  distance  is 
converted  into  a  great  force  acting  through  a  small  dis- 
tance, or  else  a  great  force  acting  through  a  small  distance 
is  converted  into  a  small  force  acting  through  a  great 
distance. 

When  a  small  force,  by  acting  through  a  great  distance, 
is  made  to  raise  a  great  weight,  or  do  a  great  deal  of  work, 
there  is  said  to  be  a  gain  of  power. in  the  machine.  When 
on  the  contrary  a  great  force,  in  moving  through  a  small 
distance,  lifts  only  a  small  weight,  or  does  very  little  work, 
there  is  said  to  be  a  loss  of  power  in  the  machine.  But 
whenever  there  is  a  gain  in  power  there  is  a  corresponding 
loss  in  speed,  and  whenever  there  is  a  loss  in  power  there 
is  a  corresponding  gain  in  speed.  For  if  in  the  machine 
a  power  of  one  pound  is  made  to  move  a  weight  of  ten 
pounds,  then  the  weight  moves  only  one  tenth  as  fast  as 
the  power.  But  when  a  power  of  ten  pounds  is  made  to 
move  a  weight  of  one  pound,  then  the  weight  moves  ten 
times  as  fast  as  the  power. 

88.  Gain  and  Loss  of  Power  in  the  Lever.  •—  In  a  lever 
of  the  first  kind,  when  the  fulcrum  is  just  halfway  between 
the  weight  and  power,  there  is  neither  gain  nor  loss  in 
power.    If  the  fulcrum  is  nearer  the  weight  than  the  power, 
then  there  will  be  a  gain  in  power  and  a  loss  in  speed.     If 
the  fulcrum  is  nearer  the  power  than  the  weight,  there  is 
loss  in  power  and  gain  in  speed. 


76  NATURAL    PHILOSOPHY. 

In  a  lever  of  the  second  kind,  the  power  is  always  far- 
ther from  the  fulcrum  than  the  weight,  and  consequently 
it  always  moves  through  greater  distance.  Hence  in  this 
kind  of  lever  there  is  always  a  gain  in  power  and  a  loss 
in  speed. 

In  a  lever  of  the  third  kind,  the  weight  is  always  farther 
from  the  fulcrum  than  the  power,  and  consequently  the 
weight  always  moves  through  the  greater  distance.  There 
is  therefore  in  this  kind  of  lever  always  a  loss  in  power 
and  a  gain  in  speed. 

89.  The  Compound  Lever,  —  Sometimes  two  or  more  sim- 
ple levers  are  combined,  as  shown  in  Figure  54.     Suppose 
that  P  be  five  times  as  far  from  the  fulcrum  f  as  A  is,  the 
point  P  will  then  move  five  times  as  fast  as  the  point  A, 
and  a  pull  of  one  pound  on  P  will  exert  a  pull  of  five 

pounds  on  A.     If  B  is  five 
lg'  54'  times   as   far   from  the  ful- 

crum F  as  W  is,  the   five 

B  __p pounds  of  pull  on  B   will 

exert  twenty-five  pounds  of 
pull  at   W.      In   this  case, 
one  pound  of  pull   exerted 
at  P  will   balance   twenty- 
five  pounds  at  W.     But  it  would  be  found  on  trial  that  on 
pulling  P  down  one  inch,  W  would  be  raised  only  one 
twenty-fifth  of  an  inch. 

Such  a  combination  of  levers  is  called  a  compound  lever. 

90.  Bent  Levers.  —  Sometimes  the  arms  of  the  lever  are 
bent,  as  shown  in  Figure  55.     In  such  a  lever  the  lengths 
of  the  arms  are  straight  lines  drawn 

from  the  fulcrum  at  right  angles  to 
the  lines  -which  show  the  direction 
in  which  the  power  and  weight  act.  ( 

The  common  claw-hammer,  as  used  for  drawing  nails, 
is  an  illustration  of  this  kind  of  lever. 


NATURAL    PHILOSOPHY. 


77 


THE  WHEEL  AND   AXLE. 

91.  When  a  weight  is  raised  by  means  of  the  lever,  it 
can  be  raised  but  a  short  distance  at  a  time.     After  rais- 
ing the  weight  a  little  way  it  must  be  propped  up,  and 
the  lever  must  be  readjusted.     On  this  account  the  lever 
cannot  be  conveniently  used  when  a  weight  is  to  be  raised 
a  considerable  distance. 

92.  The  Rack  and  Pinion.  —  In  Figure  56  we  have  a 
machine   called    the    rack   and  pinion. 

It  consists  of  the  crank  A,  which  can 

be  made  to  turn  a  small  toothed  wheel 

called    the   pinion.       On    turning    the 

pinion,    its    teeth    one    after    another 

catch  under   the   teeth    of    an    upright 

bar  B,  and  each  tooth  raises  the  bar  a 

little.     This    upright  bar  is  called  the 

rack.     On  turning  the  crank,  then,  the 

rack  rises  without  interruption ;  and  if  the  rack  is  placed 

under  the  weight,  it  will  carry  up  the  weight  as  it  rises. 

As  the  weight  can  thus  be  raised  the  length  of  the  rack 

without  interruption,  the  rack  and   pinion  is  much  more 

convenient  than  the  simple  lever,  when  the  weight  is  to 

be  raised  a  considerable  distance. 

93.  The  Rack  and  Pinion  is  a  Modification  of  the  Lever, 
in  which  the  Pinion  takes  the  Place  of  the  short  Arm.  — 
In  the  rack  and  pinion,  the  crank  takes  the  place  of  the 
long  arm  of  the   lever ;  the  rod  or  axle  upon  which  the 
pinion   turns    takes   the   place   of  the  fulcrum ;  and    the 
pinion   takes    the   place  of  the   short  arm.     Each    tooth 
of  the  pinion  is  in  fact  the  short  arm  of  a  lever  of  which 
the  crank  is  the  long  arm,  and  the  pinion   fs  a^  contriv- 
ance  by  which  the  lever  is  furnished  with  several    short 
arms   instead  of  one.     The  advantage  of  multiplying  the 


7  8  NATURAL    PHILOSOPHY. 

short  arm  in  this  way  is  this :  when  a  short  arm  has 
raised  the  weight  as  far  as  it  can,  it  is  not  necessary  to 
prop  up  the  weight  and  readjust  the  lever,  for  the  next 
short  arm  then  comes  in  play  and  raises  the  weight  far- 
ther, and  so  on. 

94.  The  Windlass.  —  Another  way  to  multiply  the  short 
arms  of  a  lever  would  be  to  fill  up  the  space  between 
the  teeth  of  the  pinion  so  that  it  may  become  a  barrel, 
and  then  fasten  the  weight  to  one  end  of  a  rope,  the 
other  end  of  which  is  fastened  to  this  barrel.  On  turn- 
ing the  crank  the  rope  would  be  wound  upon  the  barrel 
and  the  weight  raised.  The  machine  just  described  is 
called  the  windlass,  and  is  shown  in  Figure  57. 

Fig>  S7>  In  the  windlass,  the  length  of 

the  short  arm  is  the  distance 
from  the  circumference,  or  out- 
side, of  the  barrel  to  its  centre. 
This  distance  is  called  the  ra- 
dius of  the  barrel,  and  in  the 
barrel  there  are  as  many  short 
arms  as  there  are  radii.  The  length  of  the  long  arm  of 
the  lever  is  the  length  of  the  crank.  If  the  crank  were 
ten  times  as  long  as  the  radius  of  the  barrel,  a  power 
of  one  pound  at  the  end  of  the  crank  would  exert  a 
force  of  ten  pounds  at  the  circumference  of  the  barrel. 
On  turning  the  crank  round  once,  it  is  evident  that 
the  end  of  the  crank  would  move  through  a  path  like 
that  shown  by  the  dotted  line  in  Figure  56,  and  that  this 
path  would  be  ten  times  as  long  as  the  circumference 
of  the  barrel.  On  turning  the  crank  once  round,  the 
rope  would  be  wound  round  the  barrel  once,  and  the 
weight  would  be  raised  a  distance  equal  to  the  circum- 
ference of  the  barrel.  In  this  case,  then,  the  power 
would  move  through  ten  times  the  distance  the  weight 
moves  through  in  the  same  time,  and,  according  to  the 


NATURAL    PHILOSOPHY.  79 

law  of  machines  (87),  a  power  of  one  pound  at  the  end 
of  the  crank  ought  to  balance  ten  pounds  of  weight  at 
the  circumference  of  the  barrel. 

95.  The    Capstan.  —  In    the   windlass,    the    longer   the 
crank  and  the  smaller  the  barrel,  the  greater  the  gain  of 
power.     If,  however,  the  barrel  is  made  too  small,  it  is 
not  strong  enough  to   support  the  weight ;   while  if  the 
crank  is  made  too  long,  it  cannot  be  conveniently  turned 
with  the  hand.     But  the  crank,  or  long  arm  of  the  lever, 
may  be   multiplied   in   the   same  way  as   the  short   arm 
was  multiplied  in  the  case  of  the  pinion  and  the  barrel. 
Thus  in  the  windlass,  just  described,  instead  of  one  crank 
there  may  be  a  number  of  spokes,  and  a  man  by  standing 
at  one  side  may  pull  upon  one  spoke  after  another  as  they 
come  within  his  reach,  and  thus  turn  the  barrel,  though  he 
could  not  reach  far  enough  to  turn  round  a  single  spoke,  if 
it  were  arranged  like  a  crank.     If  the  barrel  were  placed 
upright,  a  man  or  several  men  might  walk  round  it,  push- 
ing against  the  spokes.     A  windlass  arranged  in  this  way 
is  called  a  capstan,  and  is  much  used  on  board  ships. 

96.  The  Wheel  and  Axle.  —  If  the  Fig.  58. 
spokes  are  connected  so  as  to  form 

a  wheel,  as  shown  in  Figure  58,  the 
barrel  is  called  the  axle,  and  the  ma- 
chine  is  called  the  wheel  and  axle. 

In  the  wheel  and  axle,  the  radius 
of  the  wheel  is  the  long  arm  of  a 
lever,  and  the  radius  of  the  axle  is 
the  short  arm.  Therefore,  the  larger  the  wheel  and  the 
smaller  the  axle,  the  greater  the  weight  which  a  power  of 
one  pound  applied  to  the  circumference  of  the  wheel  will 
balance  on  the  axle. 

Power  may  be  applied  to  the  wheel,  either  by  means 
of  pegs  projecting  from  its  rim,  as  in  Figure  58,  or  by 
a  rope  or  band  passing  around  it,  as  in  Figure  59. 


8o  NATURAL    PHILOSOPHY. 

The  law  of  machines  (87)  may  be  readily  illustrated  by 
means  of  the  wheel  and  axle.  Suppose  that  a  rope  passes 
over  the  wheel  and  another  over  the  axle,  and  that  the 
radius  of  the  wheel  is  eight  times  as  long  as  that  of  the 
axle.  On  hanging  a  weight  of  one  pound  to  the  rope 
from  the  wheel,  it  will  be  found  that  a  weight  of  eight 
pounds  must  be  hung  to  the  rope  from  the  axle  in  order 
to  balance  it ;  and  it  will  be  found,  on  turning  the  wheel, 
that  the  weight  hung  from  the  wheel  moves  through  eight 
inches,  while  that  hung  from  the  axle  moves  through 
one. 

97.   The  Ratchet.  —  The  ratchet   is  an   arrangement   to 

keep  the  wheel  from  turning  except  in  one  direction.     It 

consists  of  a  catch  c  (Figure  59),  which  plays  into  the  teeth 

v-  of  the  wheel  A  B.     It  thus  allows  the 

*>&  59- 

wheel  to  turn  to  the  left,  but  keeps  the 
weight  from  pulling  it  back  towards 
the  right. 

98.  Wheel-work.  —  In  the  wheel  and 
axle,  the  larger  the  wheel  and  the 
smaller  the  axle,  the  greater  the  gain 
of  power.  But,  as  has  already  been 
said  (95),  if  the  barrel  is  made  very 
small,  it  may  not  be  strong  enough  ;  and  on  the  other  hand, 
if  the  wheel  is  made  very  large,  it  will  be  too  heavy  and 
take  up  too  much  room.  Instead  of  using  such  a  large 
wheel,  we  may  have  several  wheels  and  axles  acting  upon 
one  another,  like  the  levers  in  the  compound  lever  (89). 
Such  a  combination,  or  train,  of  wheels  and  axles  is  often 
called  wheel-work.  The  power  is  applied  to  the  circum- 
ference of  the  first  wheel,  the  axle  of  which  acts  upon  the 
circumference  of  the  second  wheel,  which  in  turn,  by 
means  of  its  axle,  acts  upon  the  circumference  of  the  third 
wheel,  and  so  on ;  the  weight  being  hung  to  the  axle  of  the 
last  wheel. 


NATURAL    PHILOSOPHY.  8 1 

99.  Cog  Wheels.  —  There  are  various  ways  in  which  the 
axle  of  one  wheel  is  made  to  act  on  the  circumference  of 
another.  Sometimes  the  one  turns  the  other  by  rubbing 
against  it,  or  by  friction.  The  most  common  way,  however, 
is  by  means  of  teeth  or  cogs  raised  on  the  surfaces  of  the 
wheels  and  axles.  The  cogs  on  the  wheel  are  usually 
called  teeth,  while  those  on  the  axle  are  called  leaves,  and 
the  part  of  the  axle  from  which  they  project  is  called  the 
pinion,  as  in  the  rack  and  pinion  already  described  (92). 

A  train  of  wheels  thus  arranged  is  shown  in  Figure  60. 

Fig.  60. 


100.  The  gain  of  power  by  Wheel-work.  —  In  the  train  of 
wheels  in  Figure  60,  if  the  circumference  of  the  wheel  a  is 
36  inches,  and  that  of  the  pinion  b  is  9  inches,  or  one  fourth 
as  great,  a  power  of  one  pound  at  P  will  exert  a  force  of 
four  pounds  on  b.  If  the  circumference  of  the  wheel  e  be 
30  inches,  and  that  of  the  pinion  C  10  inches,  the  four 
pounds  acting  on  the  former  will  exert  a  force  of  twelve 
pounds  on  the  latter.  If  the  circumference  of  the  wheel/ 
be  40  inches,  and  that  of  the  axle  d  8  inches,  the  twelve 
pounds  acting  on  f  will  exert  a  force  of  sixty  pounds  on 
d.  One  pound  at  P  will  then  balance  sixty  pounds  at  W. 


82 


NATURAL   PHILOSOPHY. 


Fig.  61. 


But  in  this  case,  as  in  that  of  the  windlass  (94),  it  will 
be  seen  that  what  is  gained  in  power  is  lost  in  speed  ;  since 
the  one  pound  at  P  must  move  through  sixty  inches  in  or- 
der to  raise  the  sixty  pounds  at  W  one  inch. 

Cog-wheels  which  have  their  teeth  arranged  as  in  Figure 
60  are  called  spur-wheels.  If  the  teeth  project  from  the 
side  of  the  wheel,  as  in  Figure  61, 
it  is  called  a  crown-wheel.  If  their 
edges  are  sloped,  as  in  Figure  62, 
the  wheel  is  called  a  bevel -wheel. 
Bevel  -  wheels  may  be  inclined  to 
each  other  at  any  angle.  In  all 
cases  the  lines  which  mark  the  slope 
of  the  teeth  of  the  two  wheels  will 
meet  at  the  same  point,  as  in  Figure  62. 

10 1.  Belted  Wheels.  —  Another  way  in  which  the  wheels 
and  axles  may  be  made  to  act  upon  one  another  is  by 
means  of  a  belt,  or  band,  passing  over  them  both.  They 

Fig.  62. 


may  thus  be  at  any  distance  apart,  and  may  turn  either  the 
same  way  or  contrary  ways,  according  as  the  belt  does  or 
does  not  cross  between  them.  A  cog-wheel  and  its  pinion 
must,  of  course,  always  turn  in  contrary  directions. 


NATURAL    PHILOSOPHY. 


Fig.  63. 


THE     PULLEY. 

102.  In  Figure  63  H  is  a  fixed  ring.     Through  this  a 
cord  passes,  to  which  the  weight  W  is  hung.     By  pulling 
down  the  cord  at  P,  the  weight  is  drawn  up.    It  is  often  de- 
sirable thus  to  change  the  direction  of  the  power. 

If  we  use  a  ring  for  this  purpose,  much  of  the 
power  will  be  wasted  by  the  friction,  or  rubbing, 
of  the  rope  against  the  ring.  We  may  get  rid 
of  a  good  deal  of  this  friction  by  using,  instead 
of  the  ring,  a  wheel  with  a  groove  around  it  for 
keeping  the  cord  in  place.  Such  a  wheel  is 
called  a  pulley. 

There  would  be  no  gain  in  power  by  the  use  of  the  pul- 
ley. It  is  evident  that  one  pound  on  one  side  of  the 
wheel  would  balance  just  one  pound  on  the  other  side ; 
and  that  if  the  former  were  drawn  down  one  inch,  the 
latter  would  be  drawn  up  just  one  inch. 

103.  Fixed  and  Movable  Pulleys.  —  In  Figure  64,  the 
frame  of  the  pulley  D  C  is  fastened  to  the  ceiling ;   the 
frame  of  the  pulley  A  B  rises  as  the  rope  P 

is  drawn  down.  A  pulley  like  D  C  is  called 
a  fixed  pulley ;  one  like  A  B,  a  movable 
pulley.  The  frame  of  the  pulley  is  often 
called  the  block. 

1 04.  The  Law  of  the  Pulley.  —  In  the  com- 
bination, or  system,  of  pulleys  in  Figure  64, 
it  is  evident  that  the  rope  must  have  the 
same  tension,  that  is,  must  have  the  same 

strain  upon  it,  from  one  end  to  the  other.  This  fact, 
namely,  that  a  cord  when  stretched  must  have  the  same 
strain  upon  it  throughout  its  length,  is  called  the  law  of 
the  pulley. 

105.  Systems  of  Pulleys  with  one  Rope.  —  In  Figure  64. 


Fig.  64. 


W 


84 


NATURAL    PHILOSOPHY. 


the  tension  or  strain  of  the  rope  is  equal  to  the  power  P, 
since  it  balances  the  power.  If  a  weight  of  one  pound  is 
hung  to  the  rope  at  P,  there  will  be  a  strain  of  one  pound 
on  the  part  of  the  rope  on  that  side  of  the  pulley.  There 
must  then  be  a  strain  of  one  pound  upon  the  part  of  the 
rope  between  A  and  Z>,  and  a  strain  of  one  pound  between 
B  and  H.  These  two  tensions,  A  D  and  B  If,  will  evi- 
dently sustain  a  weight  of  two  pounds  at  W.  In  this  sys- 
tem of  pulleys,  then,  a  power  of  one  pound  balances  a 
weight  of  two  pounds. 

But  in  this  case,  as  in  every  other  of  the  kind,  what  is 
gained  in  power  is  lost  in  speed.  If  the  power  P  is  drawn 
down  one  foot,  the  weight  W  will  rise  only  half  a  foot ; 
for  of  the  one  foot  added  to  the  length  of  CP,  one  half 
will  be  taken  from  A  D  and  one  half  from  B  H. 

In  the  system  of  pulleys  shown  in  Figure  65,  we  see  that 
one  pound  at  P  will  balance  three  pounds  at  W,  since  each 


Fig.  65. 


Fig.  66. 


W 


of  the  three  parts  of  the  rope  on  that  side  of  the  pulley  C 
has  a  tension  of  one  pound.  But  P  must  be  drawn  down 
three  feet  in  order  to  raise  W  one  foot. 

In  Figure  66,  we  have  a  system  of  pulleys  in  which  the 


NATURAL    PHILOSOPHY. 


weight  is  four  times  the  power ;  and  in  this  case  the  power 
evidently  moves  four  times  as  far  as  the  weight. 

1 06.  Systems  of  Pulleys  with  more  than  one  Rope.  —  Figure 
67  represents  a  system  of  pulleys,  in  which  two  ropes  are 
used.  Here  a  weight  of  four  pounds  is  balanced  by  a 
power  of  one  pound.  The  parts  of  the  rope  A  D  and  A  B 
must  each  have  a  tension  equal  to  the  power.  The  rope 
A  CB  balances  the  two  tensions,  B  P  and  B  A,  and  must 
therefore  have  a  tension  of  twice  the  power.  The  three 

Fig.  67.  Fig.  68 


tensions  supporting  the  pulley  A  amount  therefore  to  lour 
times  the  power. 

In  the  system  shown  in  Figure  68,  four  ropes  are  used. 
The  tensions  of  the  several  ropes  will  be  readily  under- 
stood from  the  numbers.  It  will  be  seen  that  in  this  case 
the  power  is  doubled  by  each  movable  pulley  which  is 
added ;  but,  as  in  all  the  systems  we  have  examined,  what 
is  gained  in  power  is  lost  in  speed. 

THE  INCLINED  PLANE. 

107.  When  a  heavy  cask  is  to  be  raised  into  a  cart  or 
dray,  a  ladder  is  often  used.  One  end  of  the  ladder  is 


86  NATURAL    PHILOSOPHY. 

placed  upon  the  cart  behind  and  the  other  end  upon  the 
ground,  and  the  cask  is  rolled  up  the  inclined  surface 
thus  formed.  In  this  way  one  man  is  able  to  raise  a 
load  of  several  hundred  weight  with  comparative  ease. 
An  inclined  surface  used  in  this  way  is  called  an  in- 
clined plane. 

We  have   examples  of  the   inclined  plane  on  a  large 

scale  in  roads. 

1 08.    The  Law  of  the  In- 

Fig>  69>  dined  Plane  the  same  as  that 

of  other  Machines.  —  In  Fig- 
ure 69  we  have  an  inclined 
plane.  W  is  the  weight, 
which  is  balanced  by  the 
power  P.  B  C  is  the 

height  of  the  inclined  plane,  and  A  C  is  its  length.  It  is 
evident  that  the  power  must  descend  a  distance  equal  to 
the  length  of  the  inclined  plane,  in  order  to  raise  the 
weight  a  distance  equal  to  its  height.  Now  it  is  found 
on  trial  that,  if  the  length  of  the  inclined  plane  is  six- 
teen feet,  and  its  height  four  feet,  a  power  of  one  pound 
will  balance  four  pounds  of  weight.  But  one  multiplied 
by  sixteen  equals  four  multiplied  by  four.  That  is,  the 
power  multiplied  by  the  distance  through  which  it  acts 
equals  the  weight  multiplied  by  the  distance  through 
which  it  is  raised.  It  follows  from  the  above,  that  the 
greater  the  length  of  the  inclined  plane,  compared  with 
its  height,  the  less  the  force  necessary  to  raise  a  weight, 
and  the  slower  the  weight  rises. 

THE   WEDGE. 

109.  Instead  of  lifting  a  weight  by  moving  it  along  an 
inclined  plane,  we  may  do  the  same  thing  by  pushing 
the  inclined  plane  under  the  weight.  When  used  in 
this  way  the  inclined  plane  is  called  the  wedge.  A 


NATURAL    PHILOSOPHY. 


nvedge  which  is  used  for  splitting  wood  has  Fis-  7°- 
usually  the  form  of  a  double  inclined  plane, 
as  in  Figure  70.  The  law  of  the  wedge  is 
the  same  as  that  of  the  inclined  plane,  but 
since  a  wedge  is  usually  driven  by  a  blow  in- 
stead of  a  force  acting  continuously,  it  is  diffi- 
cult to  illustrate  this  law  by  experiments. 

no.  Uses  of  the  Wedge.  —  The  wedge  is 
especially  useful  when  a  large  weight  is  to  be 
raised  though  a  very  short  distance.  Thus  a  tall  chim- 
ney, the  foundation  of  which  has  settled  on  one  side,  has 
been  made  upright  again  by  driving  wedges  under  that 
side.  So,  too,  ships  are  often  raised  in  docks  by  driving 
wedges  under  their  keels.  Cutting  and  piercing  instru- 
ments, such  as  razors,  knives,  chisels,  awls,  pins,  needles, 
and  the  like,  are  different  forms  of  wedges. 

THE   SCREW. 

in.  In  Figure  71  we  have  a  machine  called  the  screw. 
It  is  a  movable  inclined  plane,  in  which  the  inclined 
surface  winds  round  a  cylinder.  The  cylinder  is  the  body 
of  the  screw,  and  the  inclined  surface  is  its  thread. 

The  screw  usually  turns  in  a 
block  JV,  called  the  nut.  Within 
the  nut  there  are  threads  exactly 
corresponding  to  those  on  the 
screw.  The  threads  of  the  screw 
move  in  the  spaces  between  those 
of  the  nut. 

The  power  is  usually  applied  to 
the  screw  by  means  of  a  lever  P. 
Sometimes  the  screw  is  fixed  and 
the  nut  is  movable,  and  sometimes 
the  nut  is  fixed  and  the  screw 
movable. 


Fig.  71. 


88 


NATURAL    PHILOSOPHY. 


112.  Hunter's  Screw.  —  In  Figure  71,  if  we  turn  the  lever 
P  round  once,  the  weight  W  will  be  raised  a  distance 
equal  to  the  space  between  two  threads  of  the  screw. 
Were  the  lever  of  such  a  length  that  its  end  would  de- 
scribe a  path  10  feet  long,  and  were  the  distance  between 
two  threads  of  the  screw  \  of  an  inch,  and  were  there  no 
friction  in  the  nut,  a  power  of  one  pound  applied  to  the 
end  of  the  lever  would  exert  a  force  of  480  pounds  upon 
the  weight.  It  will  be  seen  from  this  that  the  mechanical 
advantage  of  the  screw  may  be  increased  by  increasing 
the  length  of  the  lever  by  which  it  is  turned,  or  by  bring- 
ing the  threads  closer  together.  But,  if  the  threads  are 
brought  too  near  together,  they  become  too  weak ;  while, 
on  the  other  hand,  the  machine  becomes  unwieldy  if 
the  lever  is  made  too  long.  These  objections  have  been 
obviated  in  the  differential  screw,  contrived  by  Hunter, 
and  shown  in  Figure  72.  N  is  the 
nut  in  which  the  screw  A  plays.  We 
will  suppose  that  the  threads  of  this 
screw  are  TV  of  an  inch  apart.  This 
screw  A  is  a  hollow  nut,  which  re- 
ceives the  smaller  screw  B,  the  threads 
of  which  we  will  suppose  to  be  -^  of 
an  inch  apart.  This  small  screw  is 
free  to  move  upward  and  downward, 
but  is  kept  from  turning  round  by 
means  of  the  frame -work.  If  by 
means  of  the  handle  the  larger  screw 
be  turned  round  ten  times,  and  the  smaller  screw  be  al- 
lowed to  turn  round  with  it,  the  point  W  will  rise  an 
inch.  If  we  then  turn  the  smaller  screw  ten  times 
backward,  the  point  W  will  move  down  \\  of  an  inch. 
The  effect  of  both  these  motions  will  be  to  raise  the 
point  W  T'T  of  an  inch.  But  if  the  smaller  screw  has 
been  turned  upward  ten  times  and  then  downward  ten 


NATURAL   PHILOSOPHY.  89 

times,  the  effect  is  the  same  as  if  it  had  been  kept  from 
turning.  Hence  on  turning  the  lever  round  ten  times, 
the  point  W  will  be  raised  T*T  of  an  inch,  or  the  differ- 
ence of  the  distances  between  the  threads  in  the  two 
screws,  while  the  point  E  has  been  raised  an  inch.  Ac- 
cording to  the  law  of  machines,  then,  the  pressure  at  W 
is  eleven  times  as  great  as  at  E. 

113.   The  Endless  Screw.  —  In  Figure  Fig.  73. 

73,  the  thread  of  the  screw  works  be- 
tween the  teeth  of  the  wheel.  Hence 
on  turning  the  screw  the  wheel  must 
turn.  Since  as  fast  as  the  teeth  at  the 
left  escape  from  the  screw  those  on  the 
right  come  up  to  it,  the  screw  is  acting 
upon  the  wheel  continually.  Hence  this  machine  is  called 
the  endless  screw. 

SUMMARY. 

A  machine  is  a  contrivance  by  which  force  is  made  to  do 
work.  (84.) 

In  a  machine  there  is  no  real  gain  of  force,  but  a  force 
may  be  changed  in  direction,  and  a  small  force  acting 
through  a  great  distance  may  be  converted  into  a  large 
force  acting  through  a  small  distance,  or  a  large  force  acting 
through  a  small  distance  may  be  converted  into  a  small 
force  acting  through  a  great  distance.  (87.) 

The  first  simple  machine  is  the  lever.     (84.) 

There  are  three  kinds  of  levers,  depending  upon  the  rel- 
ative position  of  the  weight,  the  fulcrum,  and  the  power. 

(85-) 

In  a  lever  of  any  kind  the  weight  and  power  will 
balance  each  other  when  the  weight  multiplied  by  the  dis- 
ance  through  which  it  moves  is  equal  to  the  power  multi- 
plied by  the  distance  through  which  it  moves.  (86.) 


90  NATURAL    PHILOSOPHY. 

It  is  the  law  of  every  machine  that  the  power  and 
weight  will  balance  each  other  when  the  power  multiplied 
by  the  distance  through  which  it  moves  is  equal  to  the 
weight  multiplied  by  the  distance  through  which  it  moves 
in  the  same  time.  (87.) 

A  compound  lever  is  a  machine  in  which  two  or  more 
simple  levers  are  combined.  (89.) 

The  rack  and  pinion  is  a  lever  whose  long  arm  appears  in 
the  crank,  and  whose  short  arm  is  multiplied  in  the  pinion. 

(9^-) 

In  the  windlass,  the  barrel  and  the  rope  take  the  place 
of  the  pinion  and  the  rack.  {93.) 

In  the  wheel  and  axle,  the  long  arm  of  the  lever  is  multi- 
plied as  well  as  the  short  one.  (96.) 

When  the  axle  is  upright  the  wheel  and  axle  is  called 
a  capstan.  (95.) 

Several  wheels  are  often  combined  so  as  to  act  upon 
one  another.  (98.) 

The  wheels  may  be  made  to  act  upon  one  another  by 
means  of  cogs,  or  by  means  of  belts.  (99,  101.) 

The  direction  in  which  a  force  acts  may  be  changed  by 
means  of  a  single  fixed  pulley.  (102.) 

In  a  system  of  pulleys,  the  mechanical  advantage  de- 
pends upon  the  fact  that  a  stretched  rope  will  have  the 
same  tension  throughout  its  whole  length.  (104.) 

A  system  of  pulleys  may  be  arranged  with  one  rope,  or 
with  several  ropes.  (105,  106.) 

The  fourth  simple  machine  is  the  inclined  plane.     (107.) 

The  fifth  simple  machine  is  the  wedge.  This  is  really 
a  movable  inclined  plane  which  is  pushed  under  the 
weight  to  be  raised.  (109.) 

The  sixth  simple  machine  is  the  screw.  This  is  also 
a  movable  inclined  plane  arranged  round  a  cylinder. 

Hunter's  differential  screw  and  the  endless  screw  are  im- 
portant modifications  of  this  simple  machine.  (111-113.) 


NATURAL   PHILOSOPHY.  91 


PROBLEMS. 

97.  In  a  lever  the  short  arm  is  5  decimetres  long,  and 
the  long  arm  61  decimetres  long.     How  far  will  the  end  of 
the  long  arm  move  while  the  end  of  the  short  arm  moves 
through  3  centimetres  ? 

98.  How  far  will  the  end  of  the  short  arm  move  while 
the  end  of  the  long  arm  is  moving  through  30  centimetres? 

99.  In  a  lever  the  short  arm  is  2  metres  long,  and  the 
long  one  50  decimetres  long.    A  power  of  2  kilogrammes  is 
applied  to  the  end  of  the  long  arm.     What  weight  at  the 
end  of  the  short  arm  will  it  balance  ? 

100.  While  the  weight  in  the  last  example  is  moving 
through  3  decimetres,  how  far  will  the  power  move? 

1 01.  A  weight  of  60  decagrammes  is  applied  at  the  end 
of  the  long  arm  of  the  lever  in  the  above  example.     What 
power  must  be  applied  at  the  end  of  the  short  arm  to 
balance  it  ? 

102.  In  a  rack  and  pinion  the  radius  of  the  pinion  is  10 
decimetres.    What  must  be  the  length  of  the  crank  in  order 
that  a  power  of  8  grammes  may  balance  300  grammes  of 
weight  ? 

103.  In  a  wheel  and  axle  the  circumference  of  the  wheel 
is  6  metres  and  that  of  the  axle  30  centimetres.      What 
weight  will  a  power  of  3  grammes  balance? 

104.  In  a  train  of  wheels  a  power  of  i  gramme  balances 
a  weight  of  43   kilogrammes.      What  distance  must  the 
power   move   through   while    the   weight    moves   through 
50  decimetres? 

105.  In  a  system  of  pulleys  a  power  of  i  gramme  balances 
a  weight  of  245  kilogrammes.     How  far  will  the  weight 
move  while  the  power  is  moving  through  i  metre? 


92 


NATURAL    PHILOSOPHY. 


HAND   POWER. 

114.  We  have  now  seen  how  forces  maybe  transformed, 
so  that  a  small  force  acting  through  a  long  distance  shall 
be  equivalent  to  a  great  force  acting  through  a  short  dis- 
tance, or  a  great  force  acting  through  a  short  distance  shall 
be  equal  to  a  small    force    acting    through  a  great    dis- 
tance.    We  next  inquire  what  are  the  sources  of  mechan- 
ical power. 

115.  Hand  Machines.  —  One  of  the  most  familiar  sources 
of  mechanical  power  is  the  human  hand.     Machines  by 
which  this  power  is  applied  to  doing  work  are  called  hand 
machines.     An  iron  crow-bar  is  one  of  the  simplest  hand 
machines.     It  is,  as  we  have  seen  (84),  a  lever  of  the  first 
or  second  kind,  according  to  the  way  in  which  it  is  used. 

The  ordinary  windlass  and  the  capstan  are  examples 
of  hand  machines  of  the  wheel  and  axle  kind  ;  while 
the  tackle  which  is  so  often  used  for  hoisting  weights  is 
an  example  of  a  hand  machine  of  the  pulley  kind. 

Fig.  74- 


1 6.    The  Crab.  —  The  crab,  shown  in  Figure  74,  is 


NATURAL    PHILOSOPHY. 


93 


Fig-  75- 


hand  machine  of  the  wheel  and  axle  class.  It  consists  of 
a  pinion  P  turned  by  two  cranks  C  and  C,  and  acting  upon 
the  toothed  wheel  W.  To  the  axis  of  this  wheel  is  fixed 
the  barrel  Z>,  to  which  the  weight  is  hung  by  the  rope  r. 

The  gain  of  power  in  this  machine  can  be  computed  by 
the  principles  already  explained.     (94,  98.) 

The  crab  is  much  used  for  setting  stone  in  the  building 
of  houses,  and  for  other  work  of  the  same  kind. 

117.  The  Derrick.  —  The  derrick  (Figure  75)  consists  of 
a  mast  M,  which-  is  kept 
upright  by  means  of  ropes, 
or  guys,  G,  G,  fastened  to 
posts  driven  into  the  earth. 
B  is  an  arm,  or  boom,  at- 
tached to  the  mast  by  a 
hinge,  and  kept  in  any  re- 
quired position  by  means 
of  the  rope  R '.  The  mast 
and  boom  serve  as  the 
supports  of  a  system'  of 
pulleys,  worked  by  a  crab 
at  the  foot  of  the  mast. 
L  is  the  load,  or  weight 
to  be  raised. 

The  system  of  pulleys 
in  the  derrick  represented 
here  is  precisely  like  that 
shown  in  Figure  65,  and 
the  mechanical  advantage 

from  its  use  will  be  the  same  as  there  explained ;  and  this, 
multiplied  by  the  mechanical  advantage  obtained  by  means 
of  the  crab,  will  give  the  whole  gain  of  power  in  the 
machine. 


94 


NATURAL    PHILOSOPHY. 


Fig.  76. 


HORSE   POWER. 

1 1 8.  The  strength  of  horses  is  employed  in  drawing 
loads  over  our  roads,  which, 
as  we  have  seen,  are  in  many 
cases  inclined  planes.  Horses 
are  often  used  in  raising 
weights  by  means  of  pulleys, 
as  shown  in  Figure  76. 

119.  Hoxse  Powers.  —  Ma 
chines  by  which  the  strength 
of  horses  is  applied  to  the  do- 
ing of  work  are  usually  called 
horse  powers.  In  some  of  these 
the  horse  walks  round  a  circle, 
turning  an  upright  shaft,  which 
may  give  motion  to  a  train  oj 
wheels  (98)  for  driving  various 
kinds  of  machinery;  or  to  a 
capstan  (95),  as  shown  in  Fig- 


ure 77 
cotton 


;  or  to  a  screw,  which  may  be  used  for  pressing 
into  bales,  or  any  similar  work. 

Fig.  77- 


In  another  class  of  horse  powers,  the  horse  is  placed  on 


NATURAL    PHILOSOPHY. 


95 


the  surface  of  a  large  horizontal  wheel,  or  on  a  movable 
platform.  In  this  case  it  is  the  road,  and  not  the  horse, 
that  travels.  One  form  of  this  kind  of  horse  power  is  shown 
in  Figure  78.  It  consists  of  a  platform  made  of  wooden 

Fig.  78. 


bars  fastened  to  a  chain,  which  passes  round  two  wheels. 
The  horse  is  put  upon  this  endless  platform,  as  it  is  called, 
and  is  harnessed  to  the  frame  of  the  machine,  as  repre- 
sented in  the  Figure.  When  the  horse  draws,  he  pushes 
the  platform  backward  with  his  feet,  and  thus  gives  motion 
to  the  wheels  round  which  it  passes.  To  these  wheels 
machinery  may  be  connected  in  any  of  the  ways  already 
described. 

WIND   POWER. 

120.  We  have  a  familiar  example  of  the  wind  as  a  source 
of  mechanical    power   in   the 
sailing  of  ships. 

These  are  rigged  so  as  to 
present  to  the  wind  a  large 
extent  of  canvas,  called  sails. 
The  wind  blowing  against 
these  urges  the  ship  forward. 

Sometimes  sails,  or  broad 
vanes  of  wood,  are  arranged 


Fig-  79- 


96 


NATURAL    PHILOSOPHY. 


on  the  arms  of  a  wheel  which  is  mounted  in  a  high  tower. 
The  wind  blowing  against  these  arms  causes  the  wheel  to 
rotate,  and  by  means  of  wheel-work  this  is  made  to  carry 
other  machinery.  Such  an  arrangement  is  called  a  wind- 
milt \  and  is  shown  in  Figure  79. 


Fig.  80. 


WATER   POWER. 

121.  Water  Wheels.  —  One  of  the  most  important 
sources  of  mechanical  power  is  that  of  falling  water. 
The  falling  or  running  water  is  made  to  turn  a  wheel, 
called  a  water  wheel,  and  this  wheel  by  means  of  bands 
or  gearing  is  made  to  work  almost  any  kind  of  ma- 
chinery. 

Water  wheels  are  of 
various  forms.  Some 
turn  on  an  upright  axis, 
and  others  on  a  hori- 
zontal axis.  The  latter 
are  called  vertical  water 
wheels  and  the  former 
horizontal  water  wheels. 

122.  Vertical  Water 
Wheels.  —  One  of  the 
most  common  forms  of 
vertical  water  wheels  is 
represented  in  Figure 

80.  It  consists  of  a  series  of  boxes,  or  buckets,  arranged 
on  the  outside  of  a  wheel  or  cylinder.  Water  is  allowed 
to  flow  into  these  buckets  on  one  side  of  the  wheel,  and 
by  its  weight  causes  the  wheel  to  turn.  The  buckets  are 
so  constructed  that  they  hold  the  water  as  long  as  possible 
while  they  are  going  down,  but  allow  it  all  to  run  out  be- 
fore they  begin  to  rise  on  the  other  side. 
A  wheel  like  this  is  called  a  breast-wheel. 


NATURAL    PHILOSOPHY.  97 

The  overshot  wheel  is  similar  to  the  breast-wheel  in 
all  respects,  except  that  the  water  is  led  over  the  top 
of  the  wheel  and  poured  into  the  buckets  on  the  other 
side. 

The  undershot  wheel  has  boards  projecting  from  its  cir- 
cumference, like  the  paddle-wheel  of  a  steamboat.  The 
water  runs  under  the  wheel,  and  turns  it  by  the  force  of 
the  current  pressing  against  the  boards. 

123.  Barker's  Mill.  —  In  Figure  81 
we    have    a   hollow   upright    cylinder,  Flg"  8lp 

with  two  horizontal  arms  at  the  bot- 
tom, and  turning  on  an  axis.  The 
cylinder  is  open  at  the  top,  but  closed 
below,  except  that  it  has  two  holes  on 
opposite  sides  of  the  arms  near  the 
end,  as  shown  in  the  Figure.  If  wa- 
ter be  poured  in  at  the  top,  the  cylin- 
der begins  to  turn  round,  and  will  con- 
tinue to  turn  as  long  as  the  supply  of 
water  is  kept  up.  If  the  holes  in  the 
arms  are  stopped  up,  the  cylinder  ceases  to  move.  This 
apparatus  is  known  as  Barker's  mill.  Its  action  is  easily 
understood  when  we  recollect  that  liquids  press  equally  in 
all  directions  (17).  If  the  holes  in  the  arms  are  plugged 
up,  the  water  presses  forward  against  the  plug ;  and  it 
presses  backward  against  the  opposite  part  of  the  arm  with 
an  equal  force.  These  two  equal  forces  acting  in  opposite 
directions  would  just  balance  each  other,  so  that  there 
would  be  no  motion.  If  now  we  remove  the  plug,  there 
will  be  no  pressure  against  that  part  of  the  arm  to  balance 
the  backward  pressure  against  the  opposite  side  ;  and  the 
arm  consequently  turns  backward.  As  the  openings  in 
the  two  arms  are  on  opposite  sides  of  the  tube,  the  back- 
ward pressure  on  each  arm  tends  to  turn  the  cylinder 
round  in  the  same  direction. 

5  G 


98  NATURAL    PHILOSOPHY. 

8z-  This  machine    is  found   to   gain  in 

power  by  bending  round  the  arms,  as 
shown  in  Figure  82  ;  for  the  water  is 
thus  made  to  press  more  powerfully 
against  the  bend  of  the  arm  as  it  flows 
through  the  tube.  It  will  be  noticed 
that  there  are  two  forces  which  tend  to  turn  the  wheel  in 
this  case;  (i)  the  reaction  proper,  caused  by  the  removal 
of  the  pressure  at  the  opening  at  the  end ;  and  (2)  the 
angular  force  of  the  current  as  it  strikes  against  the  bend 
of  the  arm. 

124.  The  Turbine  Wheel.  —  The  power  of  Barker's  mill 
(Figure  82)  would  evidently  be  increased  by  increasing  the 
number  of  the  arms.  Instead  of  these  arms  we  might 
have  curved  partitions  placed  between  two  flat  discs,  form- 
ing a  wheel,  as  shown  in  Figure 
83.  Such  a  wheel  is  called  a  reac- 
tionary turbine,  since  the  reaction- 
ary force  is  still  predominant. 

Suppose  now  that  the  discs  and 
partitions  were  cut  round  where 
the  dotted  circle  is  seen  in  the  fig- 
ure, and  that  the  outer  part  were 
supported  in  some  way  beneath, 
so  that  it  might  turn  round  freely 
while  the  central  parts  of  the  wheel  were  kept  stationary. 
If  water  were  poured  into  the  wheel  from  above,  the  outer 
part  would,  of  course,  turn  round  just  as  the  whole  wheel 
did  before  it  was  cut  in  two.  For  the  action  of  the  water 
against  the  partitions  would  evidently  be  the  same  as  be- 
fore, and  it  was  this  action  of  the  water  which  turned  the 
wheel.  And  there  would  be  this  advantage  in  the  use  of 
the  divided  wheel,  that  the  outer  part,  while  turning,  would 
not  have  to  carry  the  weight  of  the  whole  column  of  water, 
as  the  wheel  did  before  it  was  divided. 


NATURAL    PHILOSOPHY. 


Fig.  84. 


Again,  by  turning  the  inner  se'.  of  partitions  as  showa 
in  Figure  84,  the  current  is 
made  to  strike  the  outer  par- 
tition in  such  a  direction  as  to 
make  its  angular  force  the 
greatest  possible.  A  wheel 
thus  arranged  is  the  ordinary 
turbine,  and  in  it  the  angular 
force  of  the  escaping  current 
is  the  chief  motive  power.  It 
is  the  most  efficient  water- 
wheel  ever  constructed. 

A  section  of  one  form  of 

this  wheel  is  shown  in  Figure  85.  The  wheel  b  b  cor- 
responds to  the  outer  part  of  the 
wheel  in  Figure  83.  It  is  supported 
from  below  and  turns  on  an  axis,  as 
represented.  Within  this  wheel  are 
stationary  partitions  curved,  as  shown 
in  Figure  84.  These  partitions  are 
placed  at  the  bottom  of  a  large 
cylinder,  into  which  the  water  is 
brought  by  the  pipe  o.  The  water 
flows  between  the  fixed  partitions 
against  the  partitions  of  the  wheel 
b  b,  causing  it  to  turn  round  rapidly. 
The  water  is  then  discharged  at  the 
circumference  of  the  wheel  b  b. 

There  are  many  kinds  of  turbines, 
and  their  effective  power  is  from  75 
to  88  per  cent  of  that  in  the  acting 

body  of  water.  In  the  best  forms  of  overshot  and  breast 
wheels  it  is  from  65  to  75  per  cent,  and  in  undershot  wheels 
from  25  to  33  per  cent. 


IOO 


NATURAL    PHILOSOPHY. 


STEAM   POWER. 

125.  Marcefs  Globe.  —  In  Figure  86  we  have  a  stout 
brass  globe  containing  water,  and  serving  as  a  boiler.    Into 

the  top  is  fastened  a  glass  manometer 
tube  (48)  about  three  feet  long,  whose 
lower  end  dips  under  mercury  placed 
in  the  bottom  of  the  globe.  Through 
another  opening  passes  the  tube  of  a 
thermometer,  the  bulb  of  which  is  in- 
side the  globe. 

Open  the  stopcock  seen  on  the 
right  of  the  globe,  boil  the  water  for 
some  time  to  expel  the  air,  and  then 
close  the  stopcock.  As  soon  as  the 
steam  formed  by  boiling  the  water  is 
thus  prevented  from  escaping,  the 
temperature  of  the  globe  begins  to 
rise.  At  the  same  time,  the  expan- 
sive force  of  the  steam  will  increase, 
raising  the  mercury  in  the  manometer; 
and  the  hotter  the  globe  gets,  the 
higher  the  mercury  rises. 

We  see,  then,  that  when  steam  is 
formed  in  a  confined  space,  its  expan- 
—     sive  force,  or  elasticity,  increases  with 
the  temperature.  , 

126.  The  Steam  Engine.  — The  elastic  force  of  the  steam 
thus  formed  can  be  made  to  work  a  piston  by  the  arrange- 
ment shown  in  Figure  87. 

The  steam  coming  from  the  boiler  by  the  tube  x  passes 
into  the  box  d.  From  this  box  extend  two  pipes,  a  and  £, 
for  carrying  the  steam,  one  above  and  the  other  below,  the 
piston.  A  sliding  valve  y  is  so  arranged  that  it  always 


NATURAL    PHILOSOPHY. 


closes  one  of  these  pipes.  In  the  right-hand  Figure  the 
lower  pipe  b  is  open,  and  the  steam  can  pass  in  under  the 
piston  and  force  it  up.  At  the  same  time  the  steam  which 
has  done  its  work  on  the  other  side  of  the  piston  passes 
out  from  the  cylinder  through  the  pipes  a  and  O. 

Fig.  87. 


The  sliding  valve  is  connected  by  means  of  the  rod  i 
with  the  crank  of  the  engine,  so  that  it  moves  up  and  down 
as  the  piston  moves  down  and  up.  As  soon,  then,  as  the" 
piston  has  reached  the  top  of  the  cylinder,  the  sliding  valve 
is  brought  into  the  position  shown  in  the  left-hand  Figure. 
The  steam  now  passes  into  the  cylinder  above  the  piston 
through  the  pipe  a  and  forces  the  piston  down,  and  the 
steam  on  the  other  side  which  has  done  its  work  goes  out 
through  b  and  O.  The  sliding  valve  is  now  again  in  the  po- 


.    €-02-       ***.*.          NATURAL   PHILOSOPHY. 


sition  shown  in  the  right-hand  Figure,  and  the  piston  is 
driven  up  again  as  before  ;  and  thus  it  keeps  on  moving 
up  and  down,  or  in  and  out.  This  kind  of  motion  is  called 
reciprocating  motion. 

In  using  the  engine  for  doing  work,  it  is  generally  neces- 
sary to  change  this  reciprocating  motion    into    a    rotary 
one ;  that  is,  to  make  the  piston,  as  it  moves  up  and  down, 
turn  a  wheel.     This  is  usually  done  by  means  of  a  crank. 
Fig.  ss.  The  crank  is  sometimes  connected 

[^^-^^^  j=— n  with  the  piston-rod  directly,  the 
cylinder  being  placed  either  hori- 
zontally, as  shown  in  Figure  88, 
or  upright,  as  in  the  engine  represented  in  Figure  90.  In 
other  cases,  the  piston-rod  turns  the 
crank  by  means  of  a  walking-beam,  the 
arrangement  and  action  of  which  will 
be  understood  from  Figure  89.  The 
walking-beam  is  much  used  for  large 
engines,  especially  on  steamboats. 

In  Figure  90  we  have  a  picture  of 
a  small  stationary  steam-engine,  which 
will  serve  to  show  how  the  parts  of  the  machine  already 
described  are  put  together,  and  also  to  illustrate  those 
parts  which  have  not  yet  been  mentioned. 

On  the  right  is  the  cylinder  P,  which  is  supplied  with 
steam  from  the  boiler  by  the  pipe  x.  The  waste  steam  is 
carried  away  by  the  pipe  L.  Within  the  cylinder  is  the 
piston  moving  up  and  down  as  explained  above.  The 
'piston-rod  A  moves  the  crank  M,  and  thus  turns  the  axle 
D,  which  may  be  connected  with  the  machinery  to  be 
driven,  by  means  of  a  belt  X,  as  here,  or  by  a  train  of 
wheels,  or  in  various  other  ways.  Q  is  a  pump,  like  that 
shown  in  Fig.  36,  which  supplies  the  boiler  with  water, 
through  the  pipe  ft.  It  is  worked  by  the  engine  itself  by 
means  of  the  rod  g  and  the  cam,  or  eccentric,  E. 


NATURAL    PHILOSOPHY. 


103 


Fig   90. 


104  NATURAL    PHILOSOPHY. 

127.  The  Governor.  —  It  often  happens  that  the  work  to 
be  done  by  an  engine  is  liable  to  vary  in  an  irregular  way. 
Parts  of  the  machinery  which  it  drives  may  be  stopped  or 
started  at  any  moment,  or  the  work  which  the  machinery 
has  to  do  may  be  greater  at  one  time  than  another.     It  is 
very  desirable  that  there  should  be  some  means  of  regulat- 
ing the  speed  of  the  engine,  so  that  it  may  not  be  too  sud- 
denly quickened  OT  retarded  by  these  variations  in  the 
resistance  which  it  has  to  overcome.     The  governor  is  a 
simple  contrivance  by  which  the  engine  is  made  to  regu- 
late its  own  speed.     It  consists  of  two  arms,  k  r  (Figure 
90),   carrying   heavy  iron   balls,   m,  n,  at   one   end,  and 
attached  by  joints  at  the  other  end  to  the  rod  c.     The 
whole  is  made  to  rotate  by  means  of  the  bevel-wheels  a 
and  b  (100),  which  are  turned  by  the  engine  itself.     If  the 
speed  of  the  engine  is  quickened,  the  governor  rotates 
faster,  and  the  arms  and  balls  tend  to  separate  more  and 
more ;  just  as  two  balls  hung  side  by  side  will  do  when  the 
strings  by  which  they  are  held  are  twirled  by  the  hand. 
As  the  arms  spread  out  they  raise  the  ring  r,  which  slides 
freely  on  the  rod  c ;  and  as  r  rises,  it  acts  upon  the  levers 
s,  t,  and  O,  which  partially  close  valve  a  in  the  pipe  x. 
This  valve  is  seen  at  v  in  Figure  87.     The  supply  of  steam 
from  the  boiler  is  thus  diminished,  and  the  speed  of  the 
engine  is  retarded.     The   governor  now  rotates  less  rap- 
idly, the  arms  drop  a   little,  the  ring   r  slides  down,  the 
valve  in  x  is  opened  a  little  more,  letting  steam  pass  to 
the  cylinder  more  freely,  and  the  speed  of  the  engine  is 
quickened    again.      Thus    any   tendency   to   go    faster  or 
slower  corrects  itself  very  promptly  through  the  agency  of 
the  governor,  and  the  engine  runs  at  almost  exactly  the 
same  speed,  however  much  the  resistance  may  vary. 

128.  The  Fly- Wheel.  —  As  has  been  stated,  a  crank  is 
commonly  used  to  change  the  reciprocating  motion  of  the 
piston  into  a  rotary  one.     But  as  the  crank  turns  round,  it 


NATURAL    PHILOSOPHY.  105 

will  be  seen  that  there  are  two  points  where  the  piston-rod 
is  pushing  exactly  in  the  direction  of  the  point  round  which 
the  crank  moves ;  and  that  at  these  points  it  does  not  tend 
to  turn  the  crank  at  all.  There  must  therefore  be  some 
means  of  carrying  the  crank  past  these  dead  points,  as  they 
are  called.  This  is  the  office  of  the  fly-wheel  V,  a  heavy 
iron  wheel  attached  to  the  axle  D.  The  great  momentum 
of  this  heavy  mass  tends  to  carry  the  axle  round  with  a 
uniform  motion,  notwithstanding  the  variations  in  the 
power  acting  upon  it. 

129.  High  Pressure  and  Low  Pressure  Engines.  —  When 
the  steam  after  doing  its  work  in  the  cylinder  is  carried 
into  a  cold  chamber,  the  engine  is  said  to  be  of  low  press- 
ure; when  it  is  forced  out  into  the  air,  the  engine  is  said 
to  be  of  high  pressure.    In  the  former  case,  the  steam  is  con- 
densed into  water  in  the  cold  chamber,  and  a  vacuum  is 
thus  formed  behind  the  piston.      In  the  latter  case,  the 
piston  has  to  act  against  the  pressure  of  the  atmosphere, 
which,  as  we  have  learned  (38),  is  equivalent  to  a  weight 
of  15  pounds  on  each  square  inch  of  its  surface.      It  is 
evident  that  a  greater  pressure  of  steam  will  be  necessary 
to  move  the  piston  in  the  latter  case. 

130.  The  Boiler.  —  In  the  boiler  the  steam  is  produced, 
and  confined  until  it  is  used  in  moving  the  piston.    It  must 
therefore  be  capable  of  furnishing  all  the  steam  needed  by 
the  engine  in  any  given  time,  and  strong  enough  to  resist 
the  expansive  force  of  the  steam  shut  up  within  it. 

Boilers  are  usually  made  of  plates  of  wrought  iron  or 
copper  riveted  together.  Copper  is  the  best  material,  but 
iron  is  almost  always  used  on  account  of  its  cheapness. 

In  order  to  get  the  full  effect  of  the  fire,  the  hot  gas  and 
smoke  from  it  are  usually  made  to  pass  through  flues  or 
tubes  in  the  body  of  the  boiler;  and  the  water  comes 
directly  in  contact  with  these  flues  or  tubes.  This  is  il- 
lustrated in  the  Cornish  boiler,  as  it  is  called,  shown  in 
5* 


106  NATURAL    PHILOSOPHY. 

Figure  91,  and  considered  one  of  the  best  forms  of  boiler. 
Fig.  9I.  It  is  a  cylinder,  frequently 

more  than  forty  feet  long, 
and  from  five  to  seven 
feet  in  diameter,  with  two 
cylindrical  flues,  B  B,  ex- 
tending its  whole  length. 
These  flues  serve  as  the 
furnace  in  which  the  fire  is  built.  The  hot  gas  and  smoke 
after  passing  through  the  flues  are  made  to  circulate  round 
the  outside  of  the  boiler  before  escaping  into  the  chimney. 
Another  form  of  boiler  is  represented  in  Figures  92  and 
93.  This  boiler  is  cylindrical,  but  instead  of  the  flues  of 
the  Cornish  boiler,  it  has  two  long  cylindrical  tubes,  B  B, 
connected  with  it  by  upright  pipes.  These  tubes  are  ex- 
posed to  the  direct  flame  of  the  fire.  The  hot  gases  and 
smoke  after  passing  under  the  tubes  to  the  other  end  of 
the  boiler,  return  through  the  flue  C  to  the  front  again, 
and  are  finally  discharged  into  the  chimney  by  the  side 
flues  D  D. 

In  Figure  92,  6"  is  the  safety-valve.  The  weight  acting 
on  the  lever  keeps  the  valve  closed  until  the  pressure  of 
the  steam  in  the  boiler  becomes  too  great  for  safety,  when 
it  opens  and  allows  a  part  of  the  steam  to  escape,  and  thus 
reduces  the  pressure,  n  is  the  tube  through  which  water 
is  supplied  to  the  boiler ;  m  the  tube  by  which  the  steam  is 
sent  to  the  cylinder.  T  is  the  man-hole,  through  which 
workmen  can  enter  the  boiler  to  clean  or  repair  it.  s  is  an 
alarm  whistle,  so  arranged  that  it  is  opened  by  the  float  E 
when  the* water  sinks  too  low  in  the  boiler.  P  is  a  con- 
trivance for  showing  the  depth  of  water  in  the  boiler  by  the 
rising  and  falling  of  the  weight  #,  which  is  connected  by 
the  lever  with  the  float  F.  A  simpler  and  better  arrange- 
ment for  the  same  purpose  consists  of  a  strong  glass  tube 
placed  outside  the  boiler,  but  communicating  with  the 


NATURAL   PHILOSOPHY. 


107 


108  NATURAL    PHILOSOPHY. 

water  within.     The  water  in  this  tube  stands  of  course  at 
the  same  height  as  that  in  the  boiler  (18). 

Figure  94  represents  the  usual  form  of  the  boiler  of  a 
locomotive  engine.  The  furnace  or  fire-box,  A,  is  within 
the  boiler,  and  is  surrounded  by  water  except  beneath  and 
at  the  door  D.  A  large  number  of  stout  tubes  extend  from 

Fig  94- 


che  fire-box  through  the  boiler  to  the  smoke-box  B.  The 
hot  gases  and  smoke  pass  through  these  before  they  escape 
into  the  chimney.  E  is  the  steam-dome,  from  the  top  of 
which  a  large  tube  conveys  the  steam  into  the  chamber  F, 
from  which  it  passes  by  tubes  on  each  side  to  the  cylinders. 
The  waste  steam  from  the  cylinders  passes  into  the  chim- 
ney through  two  pipes  meeting  at  K,  and  thus  increases 
the  draught  of  the  furnace. 

131.  The  Locomotive  Engine. — This  machine  is  shown  in 
full  in  Figure  95.  The  boiler  X  Jf  has  just  been  described. 
D  is  the  fire-box ;  Y,  the  smoke-box ;  a,  the  tubes  con- 
necting the  two ;  O,  the  door  for  putting  in  fuel ;  ;/,  the 
glass  water-gauge,  already  described,  which  shows  the 
height  of  the  water  in  the  boiler ;  H,  the  vent-cock,  by 
which  the  water  can  be  drawn  off  from  the  boiler ;  R  jR, 
the  feeders  which  conduct  water  from  the  tender  to  two 
force-pumps  (not  seen  in  the  Figure)  by  which  it  is  forced 
into  the  boiler ;  /,  the  safety-valves,  kept  down  by  spiral 


NATURAL    PHILOSOPHY. 


109 


HO  NATURAL    PHILOSOPHY. 

springs  in  the  cases  e ;  g,  the  steam-whistle  ;  G,  a  rod 
which  controls  the  valve  7  by  which  steam  is  let  into  the 
steam-pipe  A.  The  engineer  is  represented  as  holding  in 
his  hand  the  lever  by  which  this  valve  is  opened  more  or 
less,  to  regulate  the  speed  of  the  engine.  The  steam-tube 
A  passes  through  the  boiler,  as  shown  by  the  dotted  lines, 
into  the  smoke-box,  where  it  branches  off  to  the  two  cylin- 
ders. In  this  engine  there  is  no  chamber  like  that  marked 
F  in  Figure  94.  One  of  the  cylinders  is  seen  at  F,  laid 
open  to  show  the  piston  P.  The  sliding  valve  by  which 
the  steam  is  admitted  to  the  cylinder  is  precisely  like  the 
one  figured  and  described  above  (126) ;  but,  being  behind 
F  under  the  boiler,  it  does  not  appear  here.  E  is  the  pipe 
by  which  the  waste  steam  is  discharged  into  the  smoke- 
pipe  Q.  K  is  the  connecting-rod,  by  means  of  which  the 
piston  turns  the  crank  M  on  the  axle  of  the  driving  wheels. 
In  starting  the  engine  the  valves  must  be  moved  by  hand. 
This  is  done  by  means  of  the  lever  B  and  the  rod  C.  1 1 
are  stop-cocks,  through  which  any  water  condensed  in  the 
cylinders  can  be  driven  out ;  v,  the  rod  for  opening  these 
cocks. 

The  other  parts  will  be  understood  without  any  de- 
scription. 

It  will  be  seen  that  the  locomotive  is  a  high  pressure 
engine. 

SUMMARY. 

The  human  hand  is  a  source  of  mechanical  power. 
It  maybe  used  to  work  any  of  the  simple  machines.  (115.) 

The  crab  (116)  and  the  derrick  (117)  are  hand  machines. 

The  strength  of  the  horse  is  a  second  source  of  mechan- 
ical power.  (118.) 

The  horse  is  employed  to  draw  loads  up  inclined 
planes ;  to  elevate  weights  by  means  of  pulleys  ;  to  turn 


NATURAL    PHILOSOPHY.  Ill 

a  crank  or  shaft ;  and  to  turn  a  wheel  by  treading  upon 
a  movable  inclined  surface  in  the  form  of  an  endless  plat- 
form. (119.) 

The  wind  is  a  third  source  of  mechanical  power. 

This  source  of  power  is  employed  to  propel  ships  and 
to  drive  windmills.  (120.) 

The  downward  and  lateral  pressure  of  water  is  a  fourth 
source  of  mechanical  power.  (121.) 

The  downward  pressure  of  water  is  made  to  turn  a  ver- 
tical water  wheel.  (122.) 

The  lateral  pressure  of  water  is  made  to  turn  a  horizontal 
or  reaction  water  wheel.  (123.) 

The  turbine  wheel  is  a  reaction  wheel,  and  the  most 
efficient  water  wheel  known.  (124.) 

The  elastic  force  of  steam  is  a  fifth  source  of  mechanical 
power.  (125.) 

The  machine  by  which  this  source  of  power  is  applied 
is  called  a  s-team  engine.  (126.) 

The  essential  parts  of  the  steam  engine  are  the  boiler, 
in  which  the  steam  is  generated  ;  the  cylinder,  in  which 
the  expansive  force  of  the  steam  is  made  to  work  a  piston  ; 
and  the  crank,  by  which  the  motion  of  the  piston  is  made 
to  turn  a  shaft.  (130,  126.) 

Steam  engines  may  be  either  of  high  or  low  pressure. 
(129.) 


PART    SECOND. 

SOUND,    LIGHT,    HEAT,    AND 
ELECTRICITY. 


I. 


SOUND. 


NATURE   AND    PROPAGATION   OF 
SOUND. 


SOUND-WAVES. 

i.  A  Sounding  Body  is  a  Vibrating  Body.  —  If  a  glass 
bell-jar  held  by  the  knob  be  struck  with  the  knuckle,  it 
gives  out  a  sound.  If  a  bit  of  metal,  ivory,  or  other  hard 
substance  be  placed  within  the  bell,  as  seen  in  Figure  i, 

Fig.  i. 


it  is  tossed  up  and  down  rapidly,  showing  that  the  bell  is 
vibrating. 

By  similar  experiments,  it  is  found  that  every  body  is  vi- 
brating while  giving  out  sound,  and  that  it  is  only  by  caus- 
ing a  body  to  vibrate  that  it  can  be  made  to  give  out  sound. 

2.  Sound  will  not  pass  through  a  Vacuum. — In  Figure  2, 
the  bell  B  is  suspended  by  silk  threads  under  the  receiver 
of  the  air-pump.  The  bell  is  struck  by  means  of  clock- 
work, which  can  be  set  in  motion  by  the  sliding-rod  r.  If 
the  bell  be  struck  before  exhausting  the  air,  it  can  be  dis- 
tinctly heard  ;  but  as  the  air  is  exhausted,  the  sound  be- 


SOUND. 


Fig.  2. 


comes  fainter  and  fainter,  until  at  last  it  can  hardly  be 
perceived  even  with  the  ear  close  to  the  receiver.  Sound, 
then,  cannot  pass  through  a  vacuum. 

The  slight  sound  which  is 
heard  is  transmitted  by  the 
little  air  left  in  the  receiver, 
and  by  the  cords  which  hold 
up  the  bell. 

3.  Sound  passes  through  all 
Gases.  —  If  hydrogen  or  any 
other  gas  be  now  allowed  to 
pass   into   the   receiver,    the 
sound  of  the   bell  is  heard 
again.       It   will   be   noticed 
that   the    sound   is   different 
in  different  gases. 

4.  Sound  passes    through 
Liquids    and  Solids.  —  If  a 
bell  be  put  under  water  and 
struck,  it  can  be  heard.     If 
a  person  puts  his  ear  close 
to  the  rail  of  an  iron  fence, 
and  the  rail  be  struck  at  a 
considerable      distance,      he 
hears  the  blow  twice.     The 

first  sound  comes  through  the  rail ;  the  second,  which  soon 
follows,  comes  through  the  air.  These  experiments  show 
that  sound  passes  through  liquids  and  solids. 

A  slight  scratch  upon  the  iron  rail,  which  could  not  be 
heard  at  all  through  the  air,  is  heard  distinctly  when  the 
ear  is  placed  against  the  rail ;  showing  that  the  solid  trans- 
mits the  sound  better  than  the  air.  By  placing  the  ear 
near  the  ground,  the  tramp  of  horses  or  the  tread  of  men 
can  be  heard  at  a  great  distance,  the  sound  being  conveyed 
by  the  solid  earth. 


SOUND.  t  5 

5.  Sound  is  propagated  by  means  of  Vibrations.  —  We 
have  seen  (i)  that  sound  is  produced  by  vibrations.  We 
next  inquire  how  it  is  propagated.  Let  us  first  examine 
the  condition  of  the  molecules  of  the  air  in  front  of  the 
sounding  body.  Let  the  middle  line  of  dots  in  Figure  3 

Fig.  3- 

a."      b"     c"     A"      e"  o"  p" 

•       •       •       •       •••••       •       •        •      *• 


represent  the  position  of  the  molecules  when  at  rest. 
These  molecules,  as  we  have  learned,  are  not  in  contact, 
and  they  are  kept  apart  by  an  elastic  force  acting  between 
them  like  a  bent  spring.  Now,  as  the  vibrating  surface 
moves  forward  it  pushes  the  molecules  of  the  air  before  it ; 
but,  since  it  takes  time  to  transmit  the  motion  from  mole- 
cule to  molecule,  they  do  not  all  move  on  together.  The 
lower  line  of  dots  in  the  figure  represents  their  condition 
when  the  vibrating  surface  has  ceased  to  move  forward. 
The  molecule  d  is  just  ready  to  come  to  rest,  and  the 
molecule  e  just  ready  to  begin  to  move,  while  all  the  mole- 
cules between  are  moving  forward.  It  will  be  seen  that 
the  molecules  between  a  and  e  are  crowded  together,  or 
compressed.  Just  as  the  molecule  b'  comes  to  rest,  the 
molecule  beyond  e  will  begin  to  move ;  when  c  comes  to 
rest,  the  second  molecule  beyond  e  begins  o  move ;  and 
so  on.  Thus  the  line  of  compressed  molecules  keeps  of 
the  same  length,  and  continually  moving  xvX'ward. 

Suppose  the  surface  to  be  at  rest  at  a,  and  to  move 
backward  instead   of  forward.     The  elastic    force  acting 


6  .  SOUND. 

between  the  molecules  in  front  of  it  will  cause  them  to 
follow  it  one  after  another.  If  it  is  just  as  long  in  going 
backward  as  forward,  the  molecule  e  will  be  just  ready  to 
start  when  the  molecule  a  stops.  The  upper  line  of  dots 
represents  the  condition  of  the  molecules  when  the  vibrat- 
ing surface  has  ceased  to  move  backward.  The  molecule 
a"  is  just  ready  to  stop,  and  the  molecule  e"  just  ready  to 
start,  and  the  molecules  between  are  moving  backward. 
It  will  be  seen  that  the  molecules  of  this  set  are  spread 
apart,  or  extended.  When  the  molecule  b"  is  ready  to  stop, 
the  molecule  beyond  e"  is  ready  to  start ;  and  so  on.  Thus 
it  will  be  seen  that  the  line  of  extended  particles  keeps  of 
the  same  length,  and  continually  moving  forward.  As  the 
vibrating  surface  moves  backward  the  instant  it  has  moved 
-forward,  the  set  of  extended  particles  follows  on  directly 
after  the  set  of  compressed  particles  ;  and  these  two  sets 
are  sent  out  one  after  the  other  as  long  as  the  body  is 
sounding  ;  that  is,  if  from  a''  to  e'  we  have  a  set  of  ex- 
tended particles,  from  /'  to  o"  we  shall  have  a  set  of  com- 
pressed particles,  from  o"  to  /"  a  set  of  extended  particles, 
and  so  on.  It  will  be  noticed  that  the  molecules  in  the 
first  set  are  moving  forward  ;  those  in  the  second  set, 
backward  ;  those  in  the  third  set,  forward  ;  and  so  on. 
Of  course  each  molecule  is  merely  swinging  backward  and 
forward,  or  vibrating.  We  see,  then,  that  when  a  body  is 
sounding,  the  molecules  of  air  about  it  are  made  to  vi- 
brate, and  that  they  vibrate  in  sets.  Two  successive  sets 
of  these  vibrations  constitute  what  is  called  a  wave  of 
sound  ;  that  is,  in  the  figure  the  portion  of  the  upper  line 
of  dots  from  a"  to  o"  is  a  wave.  These  sound-waves  run 
out  from  a  sounding  body  in  every  direction,  just  as  the 
waves  in  water  spread  away  in  circles  from  the  point  where 
a  stone  has  been  thrown  into  it.  So  long  as  the  sound- 
waves are  passing  through  the  air,  their  outline  is  spheri- 
cal. 


SOUND.  7 

In  like  manner,  sound  is  propagated  through  solids  and 
liquids  by  means  of  vibrations. 

Sound,  then,  is  produced  by  vibrations,  and  these  vibra- 
tions are  passed  on  from  molecule  to  molecule  through  the 
intervening  bodies  to  the  ear. 

It  will  now  be  seen  why  sound  cannot  pass  through  a 
vacuum. 

6.  The  Intensity  of  Sound  depends  upon  the  Amplitude  of 
the   Vibrations.  —  If  the   bell-jar   in    Figure    i    be  struck 
lightly,  it  will  give  out  a  faint  sound,  and  the  bit  of  metal 
will  be  but  slightly  agitated  ;  if  it  be  struck  a  harder  blow, 
it  will  give  out  a  louder  sound,  and  the  metal  will  be  more 
violently  agitated.     It  is  evident  that  in  the  latter  case  the 
bell-jar  moves  backward  and  forward  through  a  greater 
space  than  in  the  former  ;  in  other  words,  that  the  ampli- 
tude of  its  vibrations  is  greater.     The  intensity  of  sound, 
then,  depends  upon  the  amplitude  of  the  vibrations  of  the 
sounding  body. 

7.  The  Intensity  of  Sound  diminishes  as  the  Square  of  the 
Distance  of  the  Sounding  Body  increases.  —  If  we  place  a 
bell  ten  yards  off,  and  four  bells  of  the  same  size  twenty 
yards  off,  we  shall  find  that  the  sound  of  the  one  bell  will 
be  just  equal  to  that  of  the  four  bells.     At  the  distance  of 
thirty  yards,  nine  bells  would  be  necessary  to  produce  a 
sound  equal  to  that  of  the  one  bell  at  ten  yards.     Sound, 
then,  diminishes  in  intensity  as  the  square  of  the  distance 
from  the  sounding  body  increases.     This  is  as  we  should 
expect.     As  the  sound-waves  spread  away  in  all  directions 
from  the  sounding  body,  a  greater  and  greater  number  of 
particles  of  air  must   be   set  in  motion,  and  the  motion 
of  each  must  be  more  feeble ;  and,  since  the  surfaces  of 
spheres  increase  as  the  squares  of  their  radii,  the  number 
of  particles  to  be  set  in  motion  increases  as  the  square  of 
the  distance  from  the  sounding  body. 

8.  Speaking-Tubes.  —  If  the  sound-waves  are  prevented 


8  SOUND. 

from  spreading  in  all  directions,  the  particles  of  air  lose 
little  of  their  motion,  and  the  sound  little  of  its  intensity. 
Thus  Biot  found  that  through  one  of  the  water-pipes  of 
Paris  words  spoken  in  a  very  low  tone  could  be  heard  at 
the  distance  of  about  three  quarters  of  a  mile.  The  sides 
of  the  pipe  kept  the  sound-waves  from  spreading.  In  the 
same  way,  conversation  can  be  carried  on  between  distant 
parts  of  a  large  building  by  means  of  small  tubes,  called 
speaking-tubes. 

9.  Sound  travels  through  the  Air  at  the  Rate  of  1,090 
Feet  a  Second.  —  The  velocity  of  sound   in  air  has  been 
several   times    determined  by  experiment.     In   1822,   the 
French  Board  of  Longitude  chose  two  heights  near  Paris, 
and  from  the  top  of  each  fired  a  cannon  at  intervals  of 
ten  minutes  during  the  night.     The  time  between  seeing 
the  flash  and  hearing  the  report  was  carefully  noted  at 
both  stations,  and  the  average  of  the  results  showed  that 
sound  travels  through  the  air  at  the  rate  of  1,090  feet  a 
second.      In    such    experiments,    the    time   taken   by   the 
light  to  pass  between  the  stations  is  too  small  to  be  per- 
ceived. 

10.  The  Observed  and  the  Computed  Velocity  of  Sound. — 
From  the  known  elasticity  and  density  of  air,  Newton  com- 
puted  that  the  velocity  of  sound  should  be   916  feet  a 
second.     That  the  observed  velocity  is  greater  is  due  to 
the  change  in  the  elasticity  of  the  air  in  the  two  portions 
of  the  sound-wave,  owing  to  the  development  of  heat  in 
the  compressed  part  and  its  absorption  in  the  extended 
part.     That  heat  is  developed  by  compression  of  the  air 
may  be  shown   by  putting  some  tinder  in  a  fire  syringe 
(Figure  4)   and  quickly  pushing   down    the    piston  :    the 
tinder  will  take  fire.     Now  heat  increases  the  elasticity  of 
the  air,  and  the  increased  elasticity  in  the  compressed  part 
of  the  wave  has  the  same  effect  as  putting  stiffer  springs 
between  the  molecules  in  front,  so  that  they  will  impart 


SOUND.  9 

their  forward  motion  to  one  another  more  promptly  ;  while 
the  diminished  elasticity  in  the  extended  portion  has  the 
same  effect  as  placing  weaker  springs  between 
the  molecules  behind,  so  that  the  molecules  can 
also  return  more  promptly.      Thus  it  will  be  seen 
that  the  change  of  elasticity  in  the  two  portions  of 
the  wave,  by  the  development  and  absorption  of 
heat,  increases  the  rapidity  with  which  the  mole- 
cules can  impart  their  vibratory  motion  to  one  an- 
other ;  and  this  rapidity  is  the  velocity  of  sound. 

11.  The  Velocity  of  the  Sound-wave  depends  on 
the  Elasticity  as  compared  with  the  Density  of  the 
Medium.  —  As  long  as  the  elasticity  remains  the 
same,  the  velocity  of  the  sound-wave  will  be  di- 
minished   by   increasing    the   density  ;    for,    the 
greater  the   density,  the  greater  the   number  of 
molecules  to  be  put  in  motion,  and  the  slower 
the  motion  will  be  transmitted.     While  the  den- 
sity remains  the  same,  the  velocity  increases  with 
the  elasticity,  as  we  have  seen  above.     This  ex- 
plains the  fact  that  the  velocity  of  sound  at  a 

great  height  in  the  air  is  the  same  as  near  the  earth.  As 
we  ascend,  the  temperature  falls  and  the  elastic  force  of 
the  air  becomes  less,  but  the  density  of  the  air  diminishes 
at  the  same  rate.  If  the  density  and  elasticity  both  in- 
crease at  the  same  rate,  the  velocity  will  remain  the  same. 
The  greater,  then,  the  elasticity  of  the  medium  compared 
with  its  density,  the  greater  the  velocity  of  sound.  It  will 
be  shown  farther  on  how  the  velocity  of  sound  in  different 
gases  can  be  ascertained. 

12.  The  Velocity  of  Sound  in  Water  is  about  4,700  Feet  a 
Second.  —  This  was  determined  at  the  Lake  of  Geneva,  in 
1826,  by  Colladon  and  Sturm.     They  found  that,  when  a 
bell  was  struck  under  water  on  one  side  of  the  lake,  the 
sound  could  be  distinctly  heard  at  a  distance  of  nine  miles 

i* 


10  SOUND. 

on  the  other  side  by  putting  the  ear  to  one  end  of  a  tube 
whose  other  end  was  in  the  water.  It  was  thus  found  that 
the  velocity  of  sound  in  water  is  about  4,700  feet  a  second. 
The  method  of  finding  how  fast  sound  travels  in  different 
liquids  will  be  explained  in  another  place. 

13.  Sound  travels  through  Solids  faster  than  through  Air. 
—  It  is  found  by  the  experiment  with  the  iron  rail  men- 
tioned above  (4)  that  the  velocity  of  sound  in  a  solid  body 
is  greater  than  in  the  air.     It  will  be  shown  hereafter  how 
we  can  find  the  velocity  of  sound  in  solids. 

14.  On  meeting  a  Medium  of  different  Density  the  Sound- 
wave is  partially  reflected.  — The  transmission  of  vibrations 
in  a  sound-wave  from  one  particle  to  another  may  be  illus- 
trated by  means  of  two  ivory  balls  hung  side  by  side.     If 
the  balls  are   of  the  same   size,  and  one  be  raised   and 
dropped  against  the  other,  the  first  gives  up  all  its  motion 
to  the  second  and  itself  comes  to  rest.     If  the  first  ball  is 
smaller  than  the  second  and  be  let  fall  against  it,  the  sec- 
ond moves  forward  and  the  first  rebounds.     If  the  first  is 
larger  than  the  second,  it  follows  the  second  a  little  way 
and  then  falls  back  again.     In  the  first  case  the  balls  illus- 
trate the  condition  of  the  molecules  in  a  uniform  medium : 
each  molecule  gives   up  all  its  motion   to  the  next,  and 
would  come  to  rest  were  it  not  kept  vibrating  by  the  sound- 
ing body  behind.     In  such  a  medium,  then,  the  sound-wave 
moves  steadily  forward.     In  the  second  case  the  balls  il- 
lustrate the  condition  of  the  molecules  of  a  rarer  medium 
contiguous  to  those  of  a  denser  medium.    When  the  sound- 
wave meets  this  denser  medium,  the  molecules  of  the  rarer 
medium  give  up  only  a  part  of  their  motion  to  those  of  the 
denser,  and  themselves  rebound,  giving  rise  to  a  reflected 
wave.     In  the  third  case  the  balls  illustrate  the  condition 
of  the  molecules  of  a  denser  medium  contiguous  to  those 
of  a  rarer  medium.     Here  it  will  be  seen  that  the  sound- 
wave is  partially  reflected  on  meeting   a  rarer  medium. 


SOUND. 


II 


Whenever,  then,  the  sound-wave  meets  a  medium  of  differ- 
ent density,  it  is  partially  reflected. 

15.  When  a  Sound-wave  is  reflected \  the  Angle  of  Reflec- 
tion is  equal  to  the  Angle  of  Incidence.  —  In  Figure  5  we 
have  two  parabolic  mirrors,  with  a  watch  placed  in  the 

Fig.  5- 


rocus  of  the  upper  one.  The  sound-waves  spread  out 
from  the  watch,  meet  the  surface  of  the  upper  mirror,  and 
are  reflected  from  that  to  the  lower  mirror,  by  which  they 
are  again  reflected.  If  the  mirrors  are  several  yards  apart, 
it  will  be  found  that  the  ticking  of  the  watch  can  be  heard 
distinctly  on  placing  the  ear  at  a,  the  focus  of  the  lower 


1 2  SOUND. 

mirror,  though  it  cannot  be  heard  at  any  other  point  near 
that  mirror.  This  shows  that  the  reflected  sound-waves 
are  all  concentrated  at  the  point  a.  By  what  path  have 
they  reached  this  point  ?  In  Figure  6,  F  is  the  focus  of 

the  parabolic  mirror  N  A 
Flg'6'  Mt   and   the    line    A   X, 

— =^ L     passing  through  the  focus 

and  the  centre  of  the  mir- 
ror, is  called  its  axis.   The 

; z      lines  M  P  and  N  P'  are 

drawn  so  as  to  be  perpen- 
dicular to  the  surface  of 
~~""  the  mirror  at  the  points 

M  and  N.     If  we  draw 

the  lines  FMand.  F  N,  showing  the  direction  in  which  the 
sound-wave  has  travelled  from  F  to  these  points,  they  will 
make  the  same  angles  with  the  perpendiculars  as  the  lines 
ML  and  NO  drawn  parallel  to  the  axis.  This  will  be 
true  whatever  may  be  the  situation  of  the  points  J/and  N. 
If  the  sound-waves  on  meeting  this  mirror  are  all  reflected 
in  lines  parallel  to  the  axis,  they  will,  on  meeting  the  sec- 
ond mirror,  be  reflected  to  its  focus.  We  have  found,  by 
the  experiment  with  the  watch,  that  they  are  reflected  to 
the  focus  of  the  second  mirror.  They  must,  then,  have 
been  reflected  from  the  first  mirror  in  a  direction  parallel 
to  its  axis ;  and  the  angle  P  ML,  at  which  any  portion  of 
the  wave  left  the  mirror,  must  have  equalled  the  angle 
F  M  P  at  which  it  struck  the  mirror.  The  former  angle  is 
called  the  angle  of  reflection,  and  the  latter  the  angle  of  in- 
cidence. Whenever,  then,  a  sound-wave  is  reflected,  the 
angle  of  reflection  is  equal  to  the  angle  of  incidence. 

1 6.  Echoes. — When  there  is  a  sufficient  interval  between 
the  direct  and  the  reflected  sound,  we  hear  the  latter  as  an 
echo.  The  reflected  sound  has  the  same  velocity  as  the 
direct  sound,  so  that  the  echo  of  a  pistol-shot  from  the 


SOUND.  13 

face  of  a  cliff  1,090  feet  distant  is  heard  two  seconds  after 
the  explosion. 

An  echo  in  Woodstock  Park  repeats  seventeen  syllables 
by  day,  and  twenty  by  night ;  one  on  the  banks  of  the 
Lago  del  Lupo,  above  the  fall  of  Terni,  repeats  fifteen. 
The  tick  of  a  watch  may  be  heard  from  one  end  of  the 
abbey  church  of  St.  Albans  to  the  other.  In  Gloucester 
Cathedral,  a  gallery  of  an  octagonal  form  conveys  a  whis- 
per seventy-five  feet  across  the  nave.  In  the  whispering 
gallery  of  St.  Paul's,  the  faintest  sound  is  conveyed  from 
one  side  to  the  other  of  the  dome,  but  is  not  heard  at  any 
intermediate  point.  .  At  Carisbrook  Castle,  in  the  Isle  of 
Wight,  is  a  well  210  feet  deep  and  12  wide.  The  interior 
is  lined  with  smooth  masonry.  When  a  pin  is  dropped 
into  the  well,  it  is  distinctly  heard  to  strike  the  water. 

In  some  cases  the  sound  is  reflected  several  times,  and 
a  succession  of  echoes  is  heard,  each  feebler  than  the  pre- 
ceding, since  a  part  of  the  sound  is  lost  at  each  reflection. 
In  mountain  regions  such  echoes  are  common,  and  some- 
times the  effect  is  very  remarkable.  There  is  a  deep  val- 
ley called  the  Ochsenthal,  near  Rosenlaui,  in  Switzerland, 
where  the  echoes  warble  in  a  wonderful  manner. 

Sounds  are  also  reflected  from  the  clouds.  When  the 
sky  is  clear,  the  report  of  a  cannon  on  an  open  plain  is 
short  and  sharp  ;  while  a  cloud  is  sufficient  to  produce  an 
^echo  like  the  rolling  of  distant  thunder.  A  feeble  echo 
also  occurs  when  sound  passes  from  one  mass  of  air  to 
another  of  different  density.  Humboldt  relates  that,  from 
a  certain  position  on  the  plains  of  Antures,  the  sound  of 
the  great  falls  of  the  Orinoco  resembles  the  beating  of  a 
surf  upon  a  rocky  shore,  being  much  louder  by  night  than 
by  day.  This  is  not  due  to  the  greater  stillness  of  the 
night,  for  the  hum  of  insects  and  the  roar  of  beasts  ren- 
der the  night  much  noisier  than  the  day.  But  between 
the  place  where  Humboldt  was  and  the  falls  lay  a  vast 


14  SOUND. 

grassy  plain,  with  many  bare  rocks  rising  from  it.  When 
exposed  to  the  sun,  these  rocks  became  much  hotter  than 
the  adjacent  grass  ;  over  each  of  them,  therefore,  rose  a 
column  of  heated  air,  less  dense  than  that  which  sur- 
rounded it.  Thus  by  day  the  sound  had  to  pass  through 
an  atmosphere  which  frequently  changed  its  density ;  the 
partial  echoes  where  the  rare  and  dense  air  met  were  in- 
cessant, and  the  sound  was  consequently  enfeebled.  At 
.night  there  were  no  such  differences  of  temperature,  and 
the  sound-waves,  travelling  through  an  atmosphere  of  uni- 
form density,  reached  the  ear  without  any  loss  from  reflec- 
tion. 

1 7.    When  a  Sound-wave  passes  obliquely  into  a  Medium 
of  different  Density  it  is  refracted.  —  Let  a  b  (Figure  7)  be 


Fig.  7. 


Fig.  8. 


a  portion  of  a  sound-wave  moving  in  the  direction  of  the 
arrow,  and  a  c  be  the  surface  of  a  medium  O  of  different 
density  from  J/,  in  which  the  wave  has  been  moving.  If 
the  elasticity  of  O  is  such  that  the  wave  will  move  faster 
in  it  than  in  Jlft  the  portion  a  of  the  wave  which  enters  O 
first  will  move  on  faster  than  the  portion  b  while  the  latter 
is  moving  in  M.  When  a  b  is  wholly  within  O,  the  second 
arrow  shows  the  direction  in  which  it  will  be  moving ;  and 


SOUND.  15 

it  will  continue  to  move  in  this  direction  so  long  as  it  is 
wholly  in  this  medium.  When  the  direction  of  a  wave  is 
thus  bent,  it  is  said  to  be  refracted.  In  this  case  it  is  bent 
away  from  a  perpendicular  P  Q  drawn  to  the  surface  of 
the  medium  O. 

If  the  elasticity  of  O  is  such  that  the  sound-wave  moves 
slower  in  it  than  in  M,  the  portion  a  of  the  wave  (Figure 
8),  when  it  has  entered  O,  moves  slower  than  b  while  the 
latter  is  in  M.  In  this  case  it  will  be  seen  that  the  direc- 
tion of  the  wave  will  be  bent  towards  the  perpendicular 

It  is  evident  that,  if  a  b  had  not  met  the  medium  O 
obliquely,  both  ends  of  it  would  have  entered  O  at  the 
same  time,  and  its  direction  would  not  have  been  changed. 

We  see,  then,  that  when  a  sound-wave  passes  obliquely 
into  a  medium  of  different  density,  it  is  refracted,  and  that, 
if  it  travels  more  rapidly  in  the  new  medium,  it  will  be  bent 
away  from  a  perpendicular  drawn  to  the  surface  of  that 
medium  ;  while,  if  it  travels  less  rapidly  in  the  new  me- 
dium, it  will  be  bent  towards  a  perpendicular  drawn  to  the 
surface  of  that  medium. 


Fig.  9. 


This  refraction  of  a  sound-wave  has  been  shown  by  the 
experiment  illustrated  in  Figure  9.  B  is  a  collodion  bal- 
loon filled  with  carbonic  acid  gas ;  w  is  a  watch  hung  near 


i6 


SOUND. 


Fig.  10. 


it ;  and  f  is  a  glass  funnel.  By  placing  the  ear  at  f  and 
moving  the  funnel  about,  a  point  will  be  found  where  the 
ticking  of  the  watch  will  be  louder  than  elsewhere.  This 
shows  that  the  sound-waves  have  been  converged  to  that 
point. 

Figure  10  shows  how  the  sound-waves  are  refracted  in 
passing  through  the  carbonic  acid,     a  b  is  a  portion  of  the 

sound-wave.  In  passing  into 
the  carbonic  acid,  —  a  me- 
dium in  which  it  moves 
more  slowly  than  in  air,  — 
it  is  bent  into  the  form  of 
m  o'  n.  On  passing  out 
from  the  carbonic  acid,  it 
is  bent  still  farther  in  the 
same  direction,  and  thus 
the  two  parts  of  the  wave 
are  made  to  converge. 


SUMMARY. 

Sound  originates  in  a  vibrating  body,     (i.) 

It  is  not  propagated  through  a  vacuum.     (2.) 

It  is  propagated  through  all  elastic  substances,  whether 

gases,  liquids,  or  solids,  by  vibrations  of  their  molecules. 

These  molecules  vibrate  in  systems,  giving  rise  to  waves. 

(3,  4.) 

Sound  is  propagated  by  vibrations.     (5.) 

Its  intensity  increases  with  the  amplitude  of  the  vibra- 
tions, and  diminishes  as  the  square  of  the  distance  from 
the  sounding  body  increases.  (6,  7). 

The  velocity  of  sound  in  air  is  1,090  feet  a  second.    (9.) 

Its  observed  velocity  is  greater  than  its  velocity  as  com- 
puted by  Newton,  owing  to  the  heat  developed  in  the 
compressed  portion  of  the  wave.  (10.) 


SOUND.  1 7 

The  velocity  of  sound  in  any  medium  depends  upon  its 
density  as  compared  with  its  elasticity,  (n.) 

The  velocity  of  sound  in  water  is  about  4,700  feet  a 
second.  Its  velocity  in  solids  is  greater  than  in  the  air. 

On  meeting  a  medium  of  different  density,  the  sound- 
waves are  partially  reflected  and  partially  transmitted. 
The  transmitted  portion  is  refracted,  unless  the  wave 
meets  the  surface  of  the  medium  perpendicularly.  (14,  17.) 

Echoes  are  due  to  reflected  sound-waves.     (16.) 


Fig.  ii. 


MUSICAL   SOUNDS. 

1 8.  Difference  between  Noise  and  Musical  Sounds.  —  In 
Figure  n  we  have  an  instrument  called  fat  gyroscope,  con- 
sisting mainly  of  a  heavy  brass  ring  d  surrounding  a  disc 
which  rests  upon  a  steel 
axis.  To  this  axis  is  fast- 
ened a  small  toothed  wheel 
W.  By  winding  a  string 
round  the  axis  and  then 
drawing  it  suddenly  out,  the 
ring  and  the  toothed  wheel 
are  made  to  spin  rapidly. 
If  a  card  c  be  held  against 
the  edge  of  the  wheel  as  it 
rotates,  a  very  shrill  musical 
sound  is  produced.  If  the 
thumb  be  placed  a  moment 
against  the  ring,  the  speed 
of  its  rotation  is  checked 
somewhat,  and  the  sound 
becomes  less  shrill.  The 
more  the  speed  is  dimin- 
ished, the  less  shrill  the 


1 8  SOUND. 

sound  becomes,  until  finally  we  hear  the  separate  taps  of 
the  teeth  against  the  card. 

We  see,  then,  that  when  the  taps  are  frequent  enough, 
they  blend  so  as  to  produce  one  continuous  sound.  Such 
a  continuous  sound  is  called  a  musical  sound. 

In  this  experiment  the  card  is  made  to  vibrate  by  strik- 
ing the  teeth  of  the  wheel,  and,  as  the  teeth  are  at  equal 
distances,  the  vibrations  follow  one  another  at  equal  inter- 
vals. A  musical  sound,  then,  is  one  in  which  the  vibra- 
tions recur  at  regular  intervals.  If  they  do  not  recur  at 
regular  intervals,  the  sound  is  called  a  noise. 

19.  The  Pitch  of  Musical  Sounds.  —  We  have  seen  that, 
the  faster  the  wheel  turns,  the  shriller  is  the  sound,  or,  in 
other  words,  the  higher  its  pitch.  Of  course,  the  faster 
the  wheel  turns,  the  more  rapid  are  the  vibrations  of  the 
card.  Hence  the  pitch  of  musical  sounds  depends  on  the 
rapidity  of  the  vibrations. 

In  musical  sounds,  as  in  all  other  sounds,  the  loudness 
depends  upon  the  amplitude  of  the  vibrations. 


20.  The  Tuning-Fork.  —  A  convenient  instrument  for 
producing  a  musical  sound  is  the  tuning-fork,  shown  in 
Figure  12.  It  consists  of  a  bar  of  steel  bent  into  the  form 


SOUND. 


Fig.  13- 


of  the  letter  Uy  and  attached  to  a  standard.  A  B  is  a 
wooden  case  open  at  both  ends,  by  which  the  intensity  of 
the  sound  produced  by  the  fork  is  increased.  The  fork 
may  be  set  vibrating  by  striking  it,  or  by  drawing  a  violin 
bow  across  it.  The  elasticity  of  the  steel  causes  the 
prongs  to  vibrate  regularly,  and  thus  to  give  out  a  musical 
sound. 

21.  The  Siren.  —  The  siren  is  an  instrument  for  pro- 
ducing musical  sounds,  and 
at  the  same  time  register- 
ing the  number  of  vibra- 
tions. It  consists  (Figure 
13)  of  a  brass  cylinder  C, 
having  a  tube  /opening  into 
it  at  the  bottom,  and  closed 
at  the  top  by  a  brass  plate 
a  b.  This  plate  is  pierced 
with  four  series  of  holes 
arranged  in  circles.  The 
innermost  series  contains 
8,  the  next  10,  the  next  12, 
and  the  last  16  holes,  d  e 
is  a  brass  disc  pierced  with 
four  series  of  holes  ar- 
ranged like  those  below. 
The  holes  in  the  plate  a  b 
are  inclined  a  little  in  one 
direction,  and  those  in  de 
a  little  in  the  opposite  di- 
rection. Through  the  cen- 
tre of  the  disc  passes  a 
steel  axis,  the  lower  end  /' 
of  which  fits  into  the  hole 
x  in  a  b.  The  disc  is  made 
to  rotate  by  blowing  into 


20 


SOUND. 


Fig.  14. 


the  tube  /.  The  current  of  air  striking  against  the  slanting 
sides  of  the  holes  in  a  b  is  directed  against  the  sides  of 
the  holes  in  d  <?,  and  thus  pushes  it  round.  As  it  rotates, 
the  holes  in  a  b  are  alternately  opened  and  closed,  so  that 
the  air  escapes  from  the  cylinder  in  a  regular  succession 

of  puffs,  giving  rise 
to  vibrations,  which 
produce  a  musical 
sound. 

The  number  of 
times  the  disc  rotates 
is  registered  by  the 
apparatus  shown  in 
the  upper  part  of  Fig- 
ure 14.  On  the  axis 
of  the  disc  is  an  end- 
less screw  s,  which  car- 
ries a  pair  of  toothed 
wheels.  These  are 
connected  with  point- 
ers moving  over  dial- 
plates  on  the  front  of 
the  instrument,  as 
shown  in  Figure  15. 

By  pushing  upon  a 
and  b  (Figure  14)  the 
registering  apparatus 
can  be  thrown  into  or 
out  of  action  at  any 
moment. 

The  stops  m,  n,  o,  /, 
seen  in  Figure  14,  are 
used  to  open  or  close  the  different  sets  of  holes. 

22.   The  Rate  at  which  a  Sounding  Body  vibrates  may  be 
determined  by  means  of  the  Siren.  — <•  If  we  force   air  into 


SOUND. 


21 


Fig.  15- 


the  siren  by  means  of  a  bellows,  the  disc  is  made  to  rotate 
faster  and  faster,  and  the  pitch  of  the  sound  produced  rises 
higher  and  higher,  as  the  force  of  the  blast  increases.  In 
this  way  the  siren  may 
be  made  to  give  a 
sound  of  the  same 
pitch  as  that  of  a  tun- 
ing-fork, or  any  other 
sounding  body  ;  and, 
by  means  of  the  regis- 
tering apparatus,  the 
number  of  vibrations 
in  a  second  may  be  as- 
certained. Suppose, 
for  instance,  that  the 
outer  set  of  holes  is 

open,  and  the  pointers  show  that  the  disc  is  making  1,440 
turns  in  a  minute.  As  there  are  16  holes  in  this  set,  there 
will  be  1 6  puffs  of  air,  or  vibrations,  for  each  turn,  or 
23,040  in  a  minute.  Dividing  this  by  60,  we  find  the 
number  of  vibrations  in  a  second  to  be  384.  If  the 
tuning-fork  is  giving  out  the  same  note  as  the  siren, 
it  is  making  384  vibrations  in  a  second. 

23.  The  Length  of  the  Sound-wave.  —  From  the  explana- 
tion given  above  (5),  it  is  evident  that  the  length  of  the 
sound-wave  is  the  distance  the  motion  is  transmitted  along 
the  line  of  molecules  while  the  sounding  body  is  making 
one  vibration.  The  faster,  then,  a  body  vibrates,  the 
shorter  is  the  sound-wave  ;  and,  as  we  know  the  velocity  of 
sound  in  air,  we  can  readily  find  the  length  of  the  sound- 
wave when  we  know  the  rate  at  which  the  body  vibrates. 
Suppose,  for  instance,  that  the  tuning-fork  is  making  384 
vibrations  in  a  second.  As  the  velocity  of  sound  in  air  is 
1,120  feet  a  second*  at  the  ordinary  temperature,  the 


*  1,090  feet  per  second  is  the  velocity  at  the  freezing  point. 


22 


SOUND. 


length  of  the  sound-wave  will  be  equal  to  1,120  divided 
by  384,  or  about  3  feet.  The  waves  produced  by  a  man's 
voice  in  ordinary  conversation  are  from  8  to  12  feet  in 
length ;  those  produced  by  a  woman's  voice,  from  2  to  4 
feet. 

24.  The  Octave.  —  If  the  outer  and  inner  circles  of  holes 
in  the  siren  are  opened,  the  two  sounds  differ  by  what 
musicians  call  an  octave.  As  there  are  16  holes  in  the 
outer  set  and  8  in  the  inner,  the  number  of  vibrations  pro- 
duced by  the  former  must  be  double  that  produced  by  the 
latter.  One  sound  is  the  octave  of  another,  then,  when  it 
is  produced  by  vibrations  twice  as  rapid. 

Fig.  16. 


25.  The  Sonometer. — Another  important  instrument  for 
investigating  the  formation  of  musical  sounds  is  the  sonom- 
eter (sound-measurer}.     The  instrument  is  shown  in  Figure 
16.     It  consists  of  the  sounding-board  M  N,  above  which 
the  string  B  B'  is  stretched  upon  two  movable  bridges  by 
means  of  the  weight  W.     It  is  used  to  illustrate  the  laws 
of  the  vibrations  of  strings. 

26.  The  Rapidity  with  which  a  String  vibrates  is  inversely 


SOUND.  23 

as  its  Length.  —  Cause  the  string  B  £'  to  vibrate  by  pulling 
it  to  one  side,  or  drawing  a  bow  across  it,  and  notice  the 
pitch  of  the  sound.  Place  one  of  the  movable  bridges  at 
the  centre  of  the  string,  so  as  to  divide  it  into  two  equal 
parts,  and  cause  either  part  to  vibrate.  The  sound  will  be 
the  octave  of  the  one  given  out  by  the  whole  string.  We 
have  already  learned  that  the  octave  of  a  note  is  produced 
by  double  the  number  of  vibrations  (24).  The  half  of  a 
string,  then,  vibrates  twice  as  rapidly  as  the  whole  string, 
when  the  tension  of  the  string  remains  the  same.  It  can, 
moreover,  be  proved,  both  by  calculation  and  by  the  siren, 
that  the  half  of  a  string  vibrates  with  exactly  twice  the 
rapidity  of  the  whole.  In  the  same  way,  it  can  be  proved 
that  one  third  of  a  string  vibrates  with  thrice  the  rapidity 
of  the  whole  ;  and  so  on.  In  general  terms,  then,  while 
the  string  is  equally  stretched,  the  rapidity  of  its  vibrations 
is  inversely  as  its  length. 

27.  The  Formation  of  Nodes •.*  —  If  we  hold  a  feather 
against  the  centre  of  the  wire  of  the  sonometer  (Figure 
17),  and  draw  a  bow  across  one  half  of  it,  we  get  the 


Fig.  17- 


octave  of  the  note  given  by  the  whole  string,  showing  that 
one  half  vibrates    by  itself.     If  now  a  little  rider  of  red 

*  See  Appendix,  I. 


24  SOUND. 

paper  be  placed  across  the  middle  of  one  part  of  the 
string,  and  the  other  part  be  made  to  vibrate  while  the 
feather  is  still  held  at  the  centre,  the  rider  is  thrown  off, 
showing  that  both  halves  of  the  string  vibrate.  These 
vibrating  halves  are  separated  by  a  node,  or  stationary  joint, 
formed  where  the  feather  touches  the  string. 

Hold  now  the  feather  one  third  of  the  way  from  the 
end  of  the  wire  (Figure  18),  and  place  a  blue  rider  on  the 

Fig.  18. 

A 


longer  portion  of  the  wire,  so  as  to  divide  it  into  two 
halves,  and  red  ones  on  the  middle  of  these  halves.  Now 
draw  the  bow  across  the  shorter  portion  of  the  wire,  and 
the  blue  rider  will  remain  at  rest  and  the  others  be 
thrown  off,  as  shown  in  the  figure  ;  showing  that  the  longer 
portion  of  the  wire  has  been  divided  into  two  vibrating 
parts  separated  by  a  node. 

Again,  place  the  feather  so  as  to  cut  off  one  fourth  of 
the  wire  (Figure  19),  and  place  blue  riders  on  the  longer 
portion  so  as  to  divide  it  into  three  equal  parts,  and  a  red 
rider  on  the  middle  of  each  of  these  parts.  Draw  the 
bow  across  the  shorter  portion  of  the  wire,  and  the  blue 
riders  will  remain  at  rest,  while  the  red  ones  are  thrown 
off,  as  seen  in  the  figure  ;  showing  that  the  longer  portion 
of  the  wire  has  been  divided  into  three  vibrating  parts 
separated  by  two  nodes. 


In  the  same  way  the  wire  may  be  divided  into  five,  six, 
or  any  number  of  vibrating  parts  separated  by  nodes. 

28.  Formation  of  Nodes  in  Vibrating  Plates.  —  In  Figure 
20  we  have  a  metallic  plate  supported  at  its  centre.  If 


Fig.  20. 


fine  sand  be  sprinkled  over  the  plate,  and  a  bow  be  drawn 
across  the  middle  of  one  edge  while  the  thumb  and  finger 
are  held  against  the  opposite  edge,  the  sand  instantly  col- 
lects into  lines,  as  seen  in  the  figure  ;  showing  that  the 
vibrating  plate  is  at  rest  along  these  lines.  The  sand  has 
all  been  tossed  away  from  the  vibrating  portions  between 
the  lines. 


26  SOUND. 

A  vibrating  plate  may,  then,  be  broken  up  into  different 
vibrating  parts,  and  the  lines  which  separate  these  parts 
are  called  nodal  lines. 

By  holding  the  thumb  and  finger  against  different  parts 
of  the  plate,  a  great  variety  of  nodal  lines  may  be  obtained, 
all  of  which  may  be  made  visible  by  means  of  sand,  as  in 
the  above  experiment.  Some  of  these  nodal  forms  are 
shown  in  Figure  21. 

Nodes  may  be  formed  in  a  similar  way  in  bells,  and  in 
all  other  sounding  bodies. 

29.  Overtones  or  Harmonics.  — We  have  now  seen  that  a 
string  or  other  sounding  body  can  either  vibrate  as  a  whole, 
or  divide  itself  into  a  number  of  equal  parts,  each  of  which 
vibrates  independently.     It  is  found  that,  even  when  it  is 
made  to  vibrate  as  a  whole,  it  always  does  at  the  same 
time  vibrate  in  parts  ;  so  that  a  vibrating  body  never  gives 
out  a  simple  tone.     The  tone  given  out  by  a  string  or 
other  body  as  a  whole  is  called  ^fundamental  note;  the 
higher  tones  produced  by  the  vibrations  of  the  parts  are 
called  harmonics  or  overtones.     The  tone  produced  by  the 
halves  of  a  string  is  called  the  first  harmonic  ;  that  pro- 
duced by  the  thirds  of  a  string,  the  second  harmonic  ;  and 
so  on. 

30.  Quality,  or  Clang-tint.  —  In  every  vibrating  string  a 
great  number  of  these  higher  tones  are  produced,  which, 
mingling  with  the  fundamental  tone,  give  rise  to  what  is 
called  the  quality  of  the  sound.     It  is  this  union  of  high 
and  low  tones  which  enables  us  to  distinguish  one  musical 
instrument  from   another.     A   flute  and    a  violin,   though 
tuned  to  the  same  fundamental  note,  do  not  give  the  same 
sound.     The  overtones  of  the  one  are  different  from  those 
of  the  other  ;  and  the  mixtures  formed  by  these  and  the 
fundamental  note  in  the  two  cases  are  therefore  different. 

Professor  Tyndall,  following  the  Germans,  calls  the  mix- 
ture of  the  fundamental  tone  and  its  overtones  a  clang,  and 


28 


SOUND. 


the  quality  of  the  clang  the  clang-tint.  Different  mixtures 
of  tones  will  have  different  clang-tints,  just  as  different 
mixtures  of  colors  have  different  tints. 

31.  The  Transmission  of  Musical  Sounds  through  Liquids. 
—  In  Figure  22,  M  is  a  long  tube  filled  with  water,  which 


is  placed  between  the  tuning-fork  F  and  the  sounding-box 
A  B.  If  the  fork  be  set  vibrating  in  the  air  away  from  the 
tube,  it  can  scarcely  be  heard  ;  but  if  the  foot  of  it  be 
placed  upon  the  water  in  the  tube,  it  can  be  heard  as  dis- 
tinctly as  when  it  is  placed  upon  the  sounding-box.  In 
both  cases  the  box  is  the  real  sounding  body,  and  is  set 
vibrating  by  means  of  the  tuning-fork.  Musical  vibrations, 
then,  are  transmitted  through  the  water  in  the  tube.  In  a 
similar  way  it  has  been  found  that  musical  sounds  are 
transmitted  through  all  liquids. 


SOUND.  29 

32.  Transmission  of  Musical  Sounds  through  Solids.  — 
Professor  Tyndall  has  shown  the  transmission  of  musical 
sounds  through  solids  by  the  following  experiment.  He 
arranged  a  wooden  rod  thirty  feet  long  so  that  it  passed 
through  a  window  in  the  ceiling  of  the  lecture-room  into 
the  open  air  above.  The  lower  end  of  the  rod  rested 
upon  a  sounding-box.  An  assistant  on  the  roof  struck  a 
tuning-fork,  but  no  sound  could  be  heard  from  it  until  he 
held  the  stem  against  the  end  of  the  wooden  rod,  when 
the  sounding-box  at  once  gave  out  a  musical  sound.  The 
pitch  of  the  sound  was  exactly  that  of  the  tuning-fork, 
showing  that  the  wood  transmitted  the  vibrations  without 
alteration.  By  using  different  forks,  notes  of  different 
pitch  were  obtained.  The  results  would  have  been  the 
same  had  the  wooden  rod  been  ten  times  as  long. 

An  experiment  first  tried  by  Wheatstone  and  repeated 
by  Tyndall  is  even  more  striking.  A  piano  was  placed  in 
a  room  underneath  the  lecture-room,  separated  from  the 
latter  by  two  floors.  Through  the  two  floors  passed  a  tin 
tube  2  J  inches  in  diameter,  with  a  wooden  rod  inside  of  it, 
the  end  of  which  projected  into  the  lecture-room.  The 
rod  was  clasped  by  India-rubber  bands  which  completely 
closed  the  tube.  The  lower  end  of  the  rod  rested  upon 
the  sounding-board  of  the  piano.  The  piano  was  played, 
and  no  sound  was  heard  in  the  lecture-room  ;  but  when  a 
violin  was  placed  against  the  end  of  the  rod,  it  became 
musical,  not  with  the  vibrations  of  its  own  strings,  but 
with  those  of  the  piano.  On  taking  away  the  violin,  the 
music  ceased  ;  but  when  a  guitar  was  put  in  its  place,  the 
sounds  were  heard  again  ;  and  also  when  a  sounding-box 
was  substituted  for  the  guitar.  The  end  of  the  rod  was 
then  placed  against  the  sounding-board  of  a  harp,  and 
every  note  of  the  piano  was  reproduced  as  before. 

An  ordinary  music-box  may  be  used  instead  of  the  piano 
in  this  experiment. 


30  SOUND. 

Musical  sounds,  then,  like  other  sounds,  are  transmitted 
unchanged  through  solids,  liquids,  and  gases. 

33.  Sympathetic  Vibrations.  —  On  the  sonometer  stretch 
two  strings  about  three  inches  asunder.  By  means  of  a 
key,  alter  the  tension  of  the  strings,  continually  sounding 
both  of  them  until  they  are  brought  into  perfect  unison. 
Place  a  little  paper  rider  upon  the  middle  of  one  of  them, 
and  agitate  the  other.  The  untouched  string  tosses  off  its 
rider,  showing  that  it  is  thrown  into  vibration. 

Every  experiment  with  the  riders  and  a  single  string 
described  above  (27)  may  be  repeated  with  these  two  uni- 
sonant  strings.  Let  us,  for  example,  damp  one  of  the 
strings  at  a  point  one  fourth  of  its  length  from  one  of  its 
ends  ;  and  let  us  place  -the  red  and  blue  riders  formerly 
employed,  not  on  the  nodes  and  vibrating  parts  of  the 
damped  string,  but  at  points  upon  the  other  exactly  oppo- 
site to  those  nodes  and  vibrating  parts.  When  the  bow  is 
passed  across  the  shorter  segment  of  the  damped  string, 
the  four  red  riders  on  the  adjacent  string  are  unhorsed, 
while  the  three  blue  ones  remain  tranquilly  in  their  places. 
Relax  one  of  the  strings  so  as  to  throw  it  out  of  unison 
with  the  other.  All  efforts  to  unhorse  the  riders  are  now 
unavailing.  Strings,  then,  can  readily  take  up  from  the 
air  those  vibrations  which  they  can  communicate  to  it,  — 
that  is,  the  vibrations  which  are  synchronous  to  their  own. 

The  influence  of  synchronism  may  be  illustrated  in  a 
still  more  striking  manner  by  means  of  two  tuning-forks 
which  sound  the  same  note.  Place  two  such  forks,  mount- 
ed on  their  resonant  supports,  upon  the  table,  18  inches 
asunder,  and  draw  the  bow  vigorously  across  one  of  them. 
If  now  we  stop  the  agitated  fork,  the  sound  is  enfeebled, 
but  by  no  means  quenched.  The  vibrations  conveyed 
through  the  air  and  through  the  wood  have  been  taken  up 
by  the  untouched  fork,  and  it  is  this  fork  which  we  now 
hear.  Attach  a  bit  of  wax  to  one  of  the  forks,  and  sound 


SOUND.  3 1 

it  again ;  the  very  slight  change  in  the  rate  of  vibration 
has  destroyed  the  sympathy  between  the  two  forks,  and  no 
response  is  now  possible.  Remove  the  wax,  and  the  un- 
touched fork  responds  as  before.  In  this  experiment  the 
forks  may  be  several  feet  apart.  The  vibrations  may  also 
be  communicated  through  the  air  alone.  Stop  one  of  the 
forks,  and  cause  the  other  to  vibrate  vigorously.  Hold 
the  case  of  the  vibrating  fork  in  the  hand,  and  bring  one 
of  its  prongs  near  the  other  fork,  placing  the  prongs  back 
to  back.  Extinguish  the  sound  of  the  agitated  fork,  and 
the  fork  which  a  moment  ago  was  silent  continues  to 
sound,  having  taken  up  the  vibrations  of  its  neighbor, 
which  must  have  been  transmitted  to  it  through  the 
air. 

Remove  one  of  the  forks  from  its  resonant  case,  and 
throw  it  into  strong  vibration.  Held  free  in  the  air,  its 
sound  is  inaudible.  But  now  bring  it  close  to  the  silent 
fork,  and  a  full,  mellow  sound  is  heard,  which  is  due,  not 
to  the  fork  first  agitated,  but  to  its  sympathetic  neighbor. 

Various  other  examples  of  the  influence  of  synchronism 
might  be  brought  forward.  If  two  clocks,  for  example, 
with  pendulums  of  the  same  period  of  vibration,  be  placed 
against  the  same  wall,  and  if  one  of  the  clocks  be  set  going 
and  the  other  not,  the  ticks  of  the  moving  clock,  trans- 
mitted through  the  wall,  will  start  its  neighbor.  The  pen- 
dulum, moved  by  a  single  tick,  swings  through  a  very 
small  arc,  but  it  returns  to  the  limit  of  its  swing  just  in 
time  to  receive  another  impulse.  In  this  way  the  impulses 
add  themselves  together  so  as  finally  to  set  the  clock  going, 
and  in  precisely  the  same  way  the  vibrating  particles  of 
wood  and  air  were  enabled  to  cause  the  string  and  fork  in 
the  above  experiment  to  vibrate.  It  is  by  this  timing  of 
impulses  that  a  properly  pitched  voice  can  cause  a  glass  to 
ring,  and  that  the  sound  of  an  organ  can  break  a  particular 
window-pane. 


32  SOUND. 

When  a  body  is  thus  thrown  into  vibration  by  its  neigh- 
bor, its  vibrations  are  said  to  be  sympathetic. 

A  body  which  could  originate  only  one  kind  of  vibration 
could  thus  intercept  only  one  kind  of  vibration  ;  while 
those  which  can  originate  vibrations  of  various  periods  can 
intercept  vibrations  of  all  these  periods.  Plates  and  mem- 
branes are  capable  of  originating  vibrations  of  the  greatest 
number  of  periods,  and  therefore  of  intercepting  the  great- 
est number  of  vibrations. 

SUMMARY. 

When  the  vibrations  of  a  sounding  body  take  place  at 
regular  intervals  and  often  enough,  they  give  rise  to  a 
musical  sound.  In  a  noise  the  vibrations  follow  one  another 
at  irregular  intervals.  (18.) 

The  pitch  of  the  sound  increases  with  the  rapidity  of  the 
vibrations.  (19.) 

The  tuning-fork  is  an  instrument  much  used  in  the  in- 
vestigation of  musical  sounds.  (20.) 

By  means  of  the  siren  we  may  ascertain  the  number  of 
vibrations  answering  to  any  given  pitch.  (22.) 

The  length  of  the  sound-wave  decreases  as  the  pitch 
rises.  (23.) 

A  string  may  vibrate  in  segments  separated  by  nodes.  (27.) 

Plates  and  all  sounding  bodies  may  vibrate  in  seg- 
ments. (28.) 

Sounding  bodies  always  break  up  into  segments  so  as  to 
start  vibrations  of  several  periods  at  the  same  time.  (29.) 

The  blending  of  these  vibrations  gives  to  the  sound  its 
quality  or  clang-tint.  (30.) 

Musical  sounds  are  transmitted  through  solids,  liquids, 
and  gases.  (31,  32.) 

Any  body  can  intercept  and  reinforce  those  vibrations 
which  are  synchronous  with  its  own.  (33.) 


SOUND.  33 


THE  SUPERPOSITION  AND  INTERFERENCE  OF  SOUND- 
WAVES. 

34.  The  Superposition  of  Water-waves.  — It  is  well  known 
that  a  great  variety  of  waves  may  exist  together  on  the  sur- 
face of  water.  Thus  in  the  ocean  we  may  have  the  great 
tidal  wave ;  upon  the  back  of  this,  the  billows  raised  by  the 
wind  ;  upon  these,  still  smaller  waves ;  and  upon  these,  in 
turn,  ripples  of  an  endless  variety  of  size  and  form.  This 
carving  of  the  surface  by  waves  and  ripples  has  its  limit  only 
in  our  powers  of  observation  ;  yet  every  wave  and  every 
ripple  retains  a  distinct  existence  amid  the  numberless 
other  motions  which  disturb  the  water. 

The  law  that  governs  this  intermingling  of  innumerable 
waves  is  that  the  resultant  motion  of  every  particle  of  water 
is  the  sum  of  the  separate  motions  given  to  it.  Thus,  any 
particle  acted  upon  by  two  forces,  both  tending  to  raise  it, 
will  be  lifted  a  distance  equal  to  the  sum  of  the  distances 
which  the  forces  acting  separately  would  raise  it.  If 
acted  upon  by  two  forces  tending  to  depress  it,  the  particle 
would  descend  a  distance  equal  to  the  sum  of  the  distances 
which  the  forces  acting  singly  would  carry  it.  If  one  of 
the  forces  tends  to  raise  the  particle,  and  the  other  to 
depress  it,  the  particle  will  move,  in  the  direction  of  the 
greater  force,  a  distance  equal  to  the  difference  of  the 
distances  which  the  forces  acting  separately  would  carry 
it.  By  the  sum  of  the  motions,  then,  we  mean  the  alge- 
braic sum. 

When  two  stones  are  cast  into  smooth  water,  20  or  30 
feet  apart,  round  each  stone  is  formed  a  series  of  expand- 
ing circular  waves,  every  one  of  which  consists  of  a  ridge 
and  a  furrow.  The  waves  at  length  touch,  and  then  cross 
one  another,  carving  the  surface  into  little  eminences  and 
depressions.  Where  ridge  coincides  with  ridge,  we  have 
2*  c 


34  SOUND. 

the  water  raised  to  a  double  height ;  where  furrow  coin- 
cides with  furrow,  we  have  it  depressed  to  a  double  depth. 
Where  ridge  coincides  with  furrow,  we  have  the  water  re- 
duced to  its  average  level.  The  resultant  motion  of  the 
water  at  every  point  is,  as  above  stated,  the  algebraic  sum 
of  the  motions  impressed  upon  that  point.  And  if,  instead 
of  two  sources  of  disturbance,  we  had  ten,  or  a  hundred,  or 
a  thousand,  the  consequence  would  be  the  same  :  the  law 
above  enunciated  would  still  hold  good. 

Instead  of  the  intersection  of  waves  from  two  distinct 
centres  of  disturbance,  we  may  cause  direct  and  reflected 
waves  from. the  same  centre  to  cross  each  other.  These 
effects  may  be  shown  by  reflecting  upon  a  screen  the  light 
from  ripples  of  water  in  a  pan.  When  mercury  is  em- 
ployed, the  effect  is  more  brilliant  still.  Here,  by  a  proper 
mode  of  agitation,  direct  and  reflected  waves  may  be  made 
to  cross  and  interlace,  and  then  again  to  disentangle 
themselves. 

Figure  23  will  give  some  idea  of  the  beauty  of  these 
effects.  It  represents  the  forms  produced  by  the  inter- 
section of  direct  and  reflected  water-waves  in  a  vessel. 
The  point  of  disturbance  is  marked  by  the  smallest  circle 
in  the  figure,  and  is  midway  between  the  centre  and  the 
circumference. 

35.  Superposition  of  Sound-waves.  —  In  like  manner  a 
great  variety  of  sound-waves  may  exist  together  in  the 
air.  For  instance,  in  the  playing  of  an  orchestra  all  the 
instruments  are  sending  forth  waves  at  the  same  time, 
which  traverse  the  air  together ;  and,  though  we  cannot 
see  them,  their  separate  existence  is  proved  by  the  fact 
that  the  ear  readily  distinguishes  the  quality  and  pitch  of 
the  sound  given  by  each  instrument.  In  this  way  thou- 
sands of  waves  may  be  transmitted  through  the  air  at  the 
same  time  without  losing  their  individual  character.  The 
same  law  holds  good  here  as  in  the  case  of  water-waves  ; 


SOUND. 


35 


namely,  that  every  particle  of  air  is  affected  by  a  motion 
which  is  the  algebraic  sum  of  all  the  single  motions  im- 
parted to  it.  The  most  wonderful  thing  of  all  is,  that 

Fig.  23. 


the  human  ear,  though  acted  upon  only  by  a  cylinder  of 
air  not  exceeding  the  thickness  of  a  quill,  can  detect 
all  the  components  of  the  motion  of  each  particle,  and 
thus  single  out  any  one  sound  from  the  confused  mixture. 

36.  Coincidence  and  Interference  of  Sound.  —  If  the  sound- 
waves, in  moving  through  the  air,  obey  the  same  laws  as 
water-waves,  they  ought,  when  meeting  in  such  a  way  that 
the  compression  of  one  coincides  with  the  compression  of 
the  other,  or  the  extension  of  one  with  the  extension  of  the 
other,  to  increase  the  volume  of  the  wave  ;  and,  on  the 
other  hand,  when  meeting  in  such  a  way  that  the  com- 
pression of  one  coincides  more  or  less  perfectly  with  the 


36  SOUND. 

extension  of  the  other,  the  volume  of  the  wave  ought 
to  be  diminished.  If  the  waves  are  exactly  alike,  and 
meet  in  exactly  opposite  phases,  one  ought  to  destroy  the 
other. 

In  Figure  24,  for  instance,  suppose  we  have  two  tuning- 
Fig.  24. 

B  A 


forks,  A  and  B,  vibrating  at  the  same  rate.  Suppose  that 
both  begin  to  vibrate  at  the  same  time,  and  that  they 
are  placed  the  length  of  a  wave  apart.  The  fork  A  will 
then  be  ready  to  start  a  wave  as  often  as  the  wave  start- 
ed by  B  reaches  it,  and  the  compressions  and  exten- 
sions of  the  successive  waves,  as  they  move  on  towards 
C,  will  coincide,  and  thus  increase  the  volume  of  the 
sound. 

Suppose  the  two  forks  A  and  B  to  be  placed  half  the 
length  of  a  wave  apart,  as  in  Figure  25.     Then  the  wave 

Fig.  25. 


sent  out  by  B  will  have  gone  twice  as  far  as  A  whenever 
A  is  ready  to  start  a  wave.  Hence  the  compression  of  the 
wave  from  B  will  coincide  with  the  extension  of  that  from 
A,  and  the  two  waves  will  destroy  each  other,  so  that  no 
sound  will  result 

If,  then,   sound-waves   interfere   like   water-waves,    two 
sounds  ought  sometimes  to  produce  silence. 


SOUND.  37 

In  Figure  26,  of  is  a  straight  tube,  which  branches  as 
represented,  and  again  unites  in  the  tube  g p.  If  a  tuning- 
fork  be  made  to  vibrate  at  <?,  the  sound  on  reaching  /  will 
divide,  a  part  running  through  the  branch  m,  and  a  part 

Fig.  26. 


through  n.  If  the  two  branches  are  of  the  same  length, 
both  portions  of  the  sound  will  reach  p  at  the  same  time. 
The  branch  n  is  made  to  slide  over  a  b,  so  that  it  can  be 
lengthened  at  pleasure.  If  n  be  made  the  length  of  half 
a  wave  longer  than  m,  no  sound  will  be  heard  at  /  /  if  it 
be  drawn  out  the  length  of  a  whole  wave,  a  sound  will  be 
heard  at  /. 

This  experiment  shows  that  two  sounds  may  produce 
silence. 

The  same  fact  can  be  illustrated  by  means  of  a  vibrating 
disc.  A  B  (Figure  27)  is  a  resonant  tube  ;  that  is,  a  tube 
which  increases  the  volume  of  sound  by  sympathetic  vibra- 
tions, as  will  be  explained  hereafter  (57).  This  tube  U 
divided  at  B.  We  have  already  learned  that,  when  a  disc 
is  vibrating,  it  breaks  up  into  parts  separated  by  nodal 
lines  (28),  and  that  the  parts  lying  side  by  side  are  vibrat- 
ing in  opposite  directions.  If  then  the  mouths  of  the 
tube  A  B  are  placed  over  two  such  parts,  the  sound-waves 
will  enter  the  tube  in  opposite  phases,  and  it  is  found 


SOUND. 


Fig.  27. 


on  trial  that  the  tube  does  not  resound.     If,  however,  the 
tube  is  placed  over  alternate  parts  of  the  disc,  which  are 

of  course  vibrating  in  the  same 
direction,  it  resounds  power- 
fully. 

The  feebleness  of  the  sound 
of  a  tuning-fork  when  held  in 
the  hand  is  due  in  a  great 
measure  to  interference.  The 
prongs  always  vibrate  in  oppo- 
site directions,  one  producing 
a  compression  where  the  other 
produces  an  extension,  and  a 
destruction  of  sound  is  the 
consequence.  By  passing  a 
pasteboard  tube  over  one  prong 
of  the  fork,  its  vibrations 
are  in  part  intercepted,  and  the  sound  becomes  louder. 
There  are  certain  positions  in  which  the  sound  of  one 
prong  is  wholly  destroyed  by  that  of  the  other.  These 
positions  are  easily  found  by  making  the  fork  vibrate,  and 
then  turning  it  round  before  the  ear.  When  the  back  or 
the  side  of  a  prong  is  parallel  to  the  ear,  the  sound  is 
heard ;  when  the  corner  of  a  prong  is  held  toward  the  ear, 
the  sound  is  utterly  destroyed. 

This  case  of  interference  may  be  rendered  more  striking 
by  means  of  a  resonant  jar.  In  Figure  28  the  jar  is  of 
such  a  length  as  to  resound  powerfully  to  the  fork.  Rotate 
the  fork  above  the  mouth  of  the  jar.  When  the  back  or 
sides  of  the  prongs  face  the  jar,  a  loud  resonance  is  ob- 
tained ;  but  when  the  corners  of  the  fork  face  the  jar,  there 
is  no  sound. 

When  the  corner  of  the  fork  is  over  the  jar,  slide  a 
pasteboard  tube  over  one  prong  so  as  to  cut  off  its  vibra- 
tions, and  the  jar  begins  to  resound. 


39 


37-  Beats.  —  If  two  tuning-forks  which  vibrate  nearly  at 
the  same  rate  be  made  to  sound  together,  it  will  be  noticed 
that  the  sound,  instead  of  being  continuous,  rises  and  falls 
in  quick  succession,  producing  what  are  called  beats.  Sup- 
pose one  of  the  forks  vibrates  240  times  in  a  second,  while 
hte  other  vibrates  246  times.  The  first  will  then  make  40 
vibrations  while  the  second  makes  41.  The  sound-waves 
which  they  generate  will  at  first  nearly  coincide  in  the  same 
phases  ;  but  they  begin  to  interfere  more  and  more,  until 
the  first  has  executed  20  vibrations,  when  they  meet  in 
opposite  phases.  The  interference  will  then  become  less 
and  less,  until  the  first  has  made  40  vibrations,  when  the 
two  sets  of  waves  will  meet  again  in  the  same  phase.  In 
this  way  a  beat  will  be  produced  at  every  4oth  vibration,  or 
6  in  a  second,  since  during  the  first  20  vibrations  the 
sound  is  growing  weaker  and  weaker,  while  during  the 
second  20  it  is  growing  louder  and  louder. 

Beats  are  thus  produced  whenever  two  musical  sounds 
of  nearly  the  same  pitch  are  uttered  together,  and  the 
number  of  beats  per  second  is  always  equal  to  the  difference 
between  the  two  rates  of  vibration. 


4° 


SOUND. 


Fig.  29. 


These  beats  may  be  il- 
lustrated by  means  of  two 
organ-pipes  (Figure  29)  of 
the  same  length.  While 
the  two  are  sounding  in 
unison,  if  the  finger  be 
brought  near  the  mouth  of 
one  so  as  to  lower  its  rate 
of  vibration,  beats  will  be 
heard. 

Beats  may  also  be  illus- 
trated by  means  of  sound- 
ing flames  (74).  Enclose 
two  such  flames  in  tubes 
provided  with  telescopic 
sliders.  If  the  tubes  are 
made  to  differ  consider- 
ably in  length,  no  beats  are 
heard,  because  the  notes 
produced  are  not  nearly 
enough  in  unison.  Gradually  lengthen  the  shorter  tube  by 
raising  the  slider.  At  first  rapid  beats  will  be  heard  ;  but 
they  will  grow  slower  and  slower,  until  the  flames  are 
brought  into  unison.  Continue  to  raise  the  slider,  and  the 
beats  are  heard  again,  slow  at  first,  but  becoming  more 
and  more  rapid,  until  they  finally  disappear. 

38.  Resultant  Tones.  —  According  to  Tyndall,  resultant 
tones  may  be  best  illustrated  by  means  of  singing  flames. 
For  this  purpose  use  two  tubes,  io§  and  II-HJ-  inches  long. 
In  addition  to  the  shrill  tones  produced  by  the  flames,  a 
very  deep  tone  may  be  detected.  Such  a  tone  is  called  a 
resultant  tone,  since  it  in  some  way  results  from  the  other 
two.  On  lengthening  one  of  the  tubes  by  means  of  a 
slider,  the  resultant  tone  gradually  rises  until  it  becomes 
quite  distinct ;  on  shortening  the  tube,  it  falls  again. 


SOUND.  41 

These  resultant  tones  may  also  be  produced  with  the 
siren.  In  this  case,  however,  as  in  all  others,  the  primary 
notes  must  be  forcible,  or  no  resultant  is  heard.  When 
the  two  series  of  holes  numbering  8  and  12  are  opened, 
the  resultant  tone  has  the  same  pitch  as  would  be  given  if 
a  series  of  4  holes  were  open.  If  we  open  two  series  of  12 
and  1 6  holes,  the  resultant  tone  is  again  the  same  as  would 
be  given  by  a  series  of  4  holes.  With  two  series  of  10  and 
1 6  holes,  the  resultant  is  the  same  as  would  be  given  by  a 
series  of  6  holes.  Thus,  in  general,  it  is  found  that  the 
pitch  of  the  resultant  tone  answers  to  a  rate  of  vibration  equal 
to  the  difference  of  the  rates  of  the  two  primaries.  From  this 
fact  these  tones  have  been  called  difference  tones. 

39.  The  Explanation  of  Resultant  Tones. — The  cele- 
brated Thomas  Young  thought  that  these  resultant  tones 
were  due  to  the  blending  of  rapid  beats,  which  linked 
themselves  together  like  the  periodic  impulses  of  an  ordinary 
musical  note.  This  explanation  was  in  harmony  with  the 
fact  that  the  number  of  the  beats,  like  that  of  the  vibra- 
tions of  the  resultant  tone,  is  equal  to  the  difference  be- 
tween the  two  sets  of  vibrations  which  produce  the  beats. 
This  explanation,  however,  is  insufficient.  The  beats  tell 
more  forcibly  upon  the  ear  than  any  continuous  sound ; 
for  when  two  notes  of  the  same  intensity  produce  beats, 
the  amplitude  of  the  vibrating  air-particles  is  at  times  de- 
stroyed, and  at  times  doubled.  But  by  doubling  the  am- 
plitude we  of  course  increase  the  intensity  of  the  sound ; 
so  that  beats  can  be  plainly  heard  when  each  of  the  two 
sounds  that  produce  them  has  ceased  to  be  audible. 

If,  therefore,  the  resultant  tones  are  due  to  the  beats  of 
their  primaries,  they  ought  to  be  heard,  even  when  the 
primaries  are  feeble ;  but  this  is  not  the  case.  This  fact 
led  Helmholtz  to  investigate  the  subject  anew.  We  have 
already  seen  that  when  several  sounds  traverse  the  same 
air,  each  particular  sound  passes  through  the  air  as  if  it 


42  SOUND. 

alone  were  present,  thus  asserting  its  own  individuality, 
and  nothing  more.  By  mathematical  investigation  Helm- 
holtz  found  that  this  is  in  strictness  true  only  when  the 
amplitudes  of  the  oscillating  particles  are  infinitely  small ; 
but  it  is  also  practically  true  when  the  disturbances  are  ex- 
tremely small.  It  is  not  true,  however,  after  they  have 
passed  a  certain  limit.  Vibrations  which  produce  a  large 
amount  of  disturbance  give  birth  to  secondary  waves,  and 
it  is  these  which  produce  resultant  tones.  Helmholtz 
found  further  that  there  should  be  also  resultant  tones 
formed  by  the  sum  of  the  primaries,  as  well  as  by  their  dif- 
ference. He  thus  discovered  his  summation  tones  before  he 
had  heard  them ;  and,  bringing  his  result  to  the  test  of  ex- 
periment, he  found  that  these  summation  tones  have  a  real 
existence.  They  cannot  be  explained  by  Young's  theory, 
but  they  find  a  complete  elucidation  in  that  of  Helm- 
holtz. 

We  see  then  that  a  coalescence  of  musical  sounds  is  far 
more  complicated  than  one  would  at  first  suppose.  For 
instance,  in  the  music  of  an  orchestra,  not  only  have  we 
the  fundamental  tones  of  every  pipe  and  of  every  string, 
but  we  have  the  overtones  of  each,  sometimes  audible  as 
far  as  the  sixteenth  in  the  series.  We  have  also  resultant 
tones;  both  difference  tones  and  summation  tones.  We 
have  fundamental  tone  interfering  with  fundamental  tone  ; 
we  have  overtone  interfering  with  overtone  ;  we  have  re- 
sultant tone  interfering  with  resultant  tone;  and,  besides  all 
this,  we  have  the  members  of  each  class  interfering  with 
the  members  of  every  other  class.  The  imagination  is 
baffled  in  the  attempt  to  conceive  the  condition  of  the  at- 
mosphere through  which  these  sounds  are  passing.  The 
aim  of  music,  through  the  centuries  during  which  it  has 
ministered  to  the  pleasure  of  man,  has  been  to  arrange 
matters  so  that  the  ear  shall  not  suifer  from  the  discord- 
ance produced  by  this  multitudinous  interference.  The 


SOUND.  43 

musicians  engaged  in  this  work  knew  nothing  of  the  phys- 
ical facts  and  principles  involved  in  their  efforts ;  they 
knew  no  more  about  it  than  the  inventors  of  gunpowder 
knew  about  the  law  of  atomic  proportions.  They  tried  and 
tried  till  they  obtained  satisfactory  results,  and  now,  when 
the  scientific  mind  is  brought  to  bear  upon  the  subject, 
these  results  are  found  to  be  in  harmony  with  natural 
law. 

SUMMARY. 

A  multitude  of  sound-waves  may  traverse  the  air  without 
losing  their  character,  in  the  same  way  as  a  multitude  of 
water-waves  may  traverse  the  surface  of  the  ocean. 

When  several  sets  of  waves  pass  through  water  or  air, 
the  motion  of  every  particle  is  the  algebraic  sum  of  the 
several  motions  impressed  upon  it.  (34,  35.) 

In  the  case  of  water,  when  the  crests  of  one  system  of 
waves  coincide  with  the  crests  of  another  system,  higher 
waves  will  be  the  result  of  the  coalescence  of  the  two  sys- 
tems. But  when  the  crests  of  one  system  coincide  with  the 
furrows  of  the  other  system,  the  two  systems  partially  or 
wholly  destroy  each  other.  (34.) 

The  same  is  true  of  sonorous  waves.  If  in  two  systems 
of  sonorous  waves  compression  coincides  with  compression, 
and  extension  with  extension,  the  sound  produced  by  such 
coincidence  is  louder  than  that  produced  by  either  system 
taken  singly.  But  if  the  compressions  of  the  one  system 
coincide  with  the  extensions  of  the  other,  a  partial  or 
total  destruction  of  both  systems  is  the  consequence.  (36.) 

This  mutual  destruction  of  two  systems  of  waves  is  called 
interference. 

When  two  musical  sounds  of  nearly  the  same  pitch  are 
sounded  together,  the  flow  of  the  sound  is  disturbed  by 
beats.  (37.) 


44  SOUND. 

These  beats  are  due  to  the  alternate  coincidence  and 
interference  of  the  two  systems  of  sonorous  waves.  If  the 
two  sounds  be  of  the  same  intensity,  their  coincidence  pro- 
duces a  sound  of  four  times  the  intensity  of  either,  while 
their  interference  produces  absolute  silence. 

The  effect,  then,  of  two  such  sounds  in  combination  is  a 
series  of  shocks,  which  we  have  called  beats,  separated 
from  one  another  by  a  series  of  pauses. 

The  rate  at  which  the  beats  succeed  one  another  is  equal 
to  the  difference  between  the  two  rates  of  vibration.  (37.) 

The  law  of  the  superposition  of  vibrations  is  strictly  true 
only  when  the  amplitudes  are  exceedingly  small.  When 
the  disturbance  of  the  air  by  a  sounding  body  is  so  violent 
that  the  law  no  longer  holds  good,  secondary  waves  are 
formed.  These  secondary  waves  give  rise  to  resultant 
tones.  (38.) 

Resultant  tones  are  of  two  kinds,  —  the  one  class  corre- 
sponding to  rates  of  vibration  equal  to  the  difference  of 
the  rates  of  the  two  primaries  ;  the  other  class  correspond- 
ing to  rates  of  vibration  equal  to  the  sum  of  the  two  pri- 
maries. The  former  are  called  difference  tones ;  the  latter, 
summation  tones.  (39.) 

CHORDS   AND   DISCORDS. 

40.  Combination  of  Musical  Sounds.  —  Take  two  tuning- 
forks,  each  of  which  gives  256  vibrations  in  a  second,  and 
set  therri  vibrating.  The  two  musical  sounds  flow  together 
in  a  perfectly  blended  stream,  and  produce  what  is  called 
unison.  In  this  instance  the  ratio  of  the  vibrations  is 
i  :  i. 

Take  now  two  forks,  one  of  which  makes  256  vibrations 
a  second,  while  the  other  makes  512.  For  every  wave, 
therefore,  sent  to  the  ear  by  the  one  fork,  two  waves  are 
sent  by  the  other,  and  the  two  notes  blend  harmoniously. 


SOUND.  45 

This  combination,  as  we  have  seen,  is  called  an  octave 
(24) ;  and  the  ratio  of  the  vibrations  is  i  :  2. 

Take  another  pair  of  forks,  which  give  256  and  384 
vibrations  in  a  second.  The  combination  of  the  two 
sounds  is  very  pleasing  to  the  ear,  but  the  consonance  is 
hardly  so  perfect  as  in  the  case  of  the  octave.  There  is  a 
barely  perceptible  roughness  here,  which  is  absent  when 
a  note  and  its  octave  are  sounded ;  but  it  is  too  slight  to 
render  the  combination  disagreeable.  The  ratio  of  the 
vibrations  is  2  :  3  ;  that  is,  one  of  the  forks  sends  two 
waves  and  the  other  three  to  the  ear  in  the  same  interval 
of  time.  This  is  the  most  pleasing  combination  next  to 
the  octave,  and  is  called  a  fifth. 

If  we  take  two  forks  whose  vibrations  are  in  the  ratio 
3  :  4,  and  sound  them  together,  the  interval  is  called  a 
fourth.  This  combination  is  still  agreeable,  but  not  quite 
so  agreeable  as  the  fifth. 

Thus,  then,  with  perfect  unison  the  ratio  of  the  vibra- 
tions is  i  :  i  ;  with  a  note  and  its  octave  it  is  1:2; 
with  a  note  and  its  fifth  it  is  2  13;  and  with  a  note  and  its 
fourth  it  is  3  :  4.  We  have  thus  gradually  developed  the 
remarkable  law  that  the  combination  of  two  notes  is  the  more 
pleasing  to  the  ear,  the  smaller  the  two  members  which  express 
the  ratio  of  their  vibrations. 

Take  now  two  forks  whose  rates  of  vibration  are  in  the 
ratio  4:5,  or  a  major  third  apart ;  the  harmony  is  less 
perfect  than  in  any  of  the  cases  which  we  have  examined. 
With  the  ratio  5  :  6,  or  that  of  a  minor  third,  it  is  usually 
less  perfect  still ;  and  we  now  approach  a  limit  beyond 
which  a  musical  ear  will  not  tolerate  the  combination  of 
two  sounds.  If,  for  example,  we  sound  together  two  forks 
whose  vibrations  are  in  the  ratio  of  13  :  14,  their  combina- 
tion is  altogether  discordant. 

An  agreeable  combination  of  two  notes  is  called  a 
chord ;  a  disagreeable  one,  a  discord. 


46  SOUND. 

41.  The  Explanation  of  Chords  and  Discords.  —  Euler's 
famous  explanation  of  the  nature  of  chords  is  as  follows  : 
We  take  delight  in  order ;  it  is  pleasant  to  us  to  observe 
"  means  co-operant  to  an  end."  But  then  the  effort  to  dis- 
cern order  must  not  be  so  great  as  to  weary  us.  If  the 
relations  to  be  disentangled  are  too  complicated,  though 
we  may  see  the  order,  we  cannot  enjoy  it.  The  simpler 
the  terms  in  which  the  order  expresses  itself,  the  greater  is 
our  delight.  Hence  the  superiority  of  the  simpler  ratios 
in  music  over  the  more  complex  ones.  Consonance,  then, 
according  to  Euler,  was  the  pleasure  derived  from  the  per- 
ception of  order  without  weariness  of  mind. 

But  in  this  theory  it  was  overlooked  that  Pythagoras, 
who  first  experimented  on  these  musical  intervals,  knew 
nothing  about  rates  of  vibration.  It  was  forgotten  that  the 
vast  majority  of  those  who  take  delight  in  music,  and  who 
have  the  sharpest  ears  for  the  detection  of  a  dissonance, 
know  nothing  whatever  about  rates  or  ratios.  And  even 
the  scientific  man  who  is  fully  informed  upon  these  points 
has  his  pleasure  in  no  way  enhanced  by  his  knowledge. 
Euler's  explanation,  therefore,  does  not  satisfy  the  mind  ; 
and  it  ^vas  reserved  for  Helmholtz  to  assign  the  physical 
cause  of  consonance  and  dissonance. 

Tyndall  illustrates  Helmholtz's  explanation  of  conso- 
nance and  dissonance  by  the  following  experiment.  He 
converts  two  jets  of  burning  gas  into  singing  flames  by 
enclosing  them  within  two  tubes.  The  tubes  are  of  the 
same  length,  and  the  flames  of  course  sing  in  unison.  By 
means  of  a  slider,  he  lengthens  slightly  one  of  the  tubes, 
and  gets  beats  which  succeed  one  another  so  slowly  that 
they  can  be  counted  with  ease.  He  lengthens  the  tube  still 
farther,  and  the  beats  become  more  rapid.  He  continues 
to  lengthen  the  tube,  and  the  beats  pass  into  a  rattle,  which 
differs  only  in  rapidity  from  the  slow  beats  heard  at  first. 
Here  we  have,  from  first  to  last,  nothing  but  an  unbroken 


SOUND.  47 

succession  of  beats.  We  begin  slowly  ;  we  gradually  in- 
crease the  speed,  until  the  succession  is  so  rapid  as  to  pro- 
duce that  peculiar  grating  effect  which  is  called  dissonance. 
If  now  we  reverse  the  process,  and  pass  from  these  quick 
beats  to  slow  ones,  the  beats  separate  from  one  another 
more  and  more,  until  finally  they  are  slow  enough  to  be 
counted.  Thus  these  singing  flames  enable  us  to  follow 
the  beats  with  certainty  until  they  cease  to  be  beats,  and 
are  converted  into  dissonance. 

This  experiment  proves  conclusively  that  dissonance 
may  be  produced  by  a  rapid  succession  of  beats. 

Helmholtz  found  that  beats  which  succeed  one  another 
at  the  rate  of  33  per  second  give  the  greatest  possible  dis- 
sonance. When  the  beats  are  slower  than  33,  they  are 
less  disagreeable.  They  may  even  become  pleasant  through 
imitating  the  trills  of  the  human  voice.  With  higher  rates 
than  33,  the  roughness  also  lessens,  but  it  is  still  dis- 
cernible when  the  beats  number  100  a  second.  The 
limit  at  which  they  totally  disappear  is  132. 

Does  this  theory  accord  with  the  facts  of  observation  ? 
We  have  found  certain  combinations  of  notes  agreeable, 
and  others  disagreeable.  Can  this  be  explained  on  the 
theory  of  Helmholtz  ?  We  must  bear  in  mind  that  musi- 
cal instruments  usually  give  overtones,  and  that  these  also 
interfere  to  produce  beats.  Let  us  start  with  the  middle  C 
of  a  piano,  and  examine  its  chords.  The  following  table 
gives  the  rates  of  the  vibrations  of  the  fundamental  tones 
and  the  first  five  overtones  of  the  octave  :  — 


Fundamental  tone         264  528     Fundamental  tone. 

Overtones     .     .     i.      528  1,056 

.     .     2.      792  1,584 

.       .       3.    1,056  2,112 

.      .      4.    1,320  2,640 

.     •     5-  ^584  3,i68 


48  SOUND. 

Comparing  these  tones  in  couples,  we  find  it  impossible 
to  get  out  of  the  two  series  a  pair  whose  difference  is  less 
than  264.  Hence,  as  the  beats  cease  to  be  heard  as  dis- 
sonance when  they  reach  132,  there  can  be  no  dissonance 
in  this  combination.  This  octave,  therefore,  is  an  abso- 
lutely perfect  consonance. 

Let  us  now  take  the  interval  of  a  fifth.     We  have  the 
following  fundamental  tones  and  overtones  :  — 

2  :         3 

Fundamental  tone  264               396     Fundamental  tone. 

Overtones     .     .     i.  528               792 

.     .     2.  792  1,188 

.     .     3.  1,056  1,584 

.     .     4-  1,320  1,980 

.     .     5.  1,584  2,376 

The  lowest  difference  here  is  132,  which  corresponds  to 
the  vanishing  point  of  the  dissonance.  The  interval  of  a 
fifth  in  this  octave  is,  therefore,  all  but  perfectly  free  from 
dissonance. 

Let  us  now  take  the  interval  of  a  fourth. 

3  :         4 

Fundamental  tone         264  352     Fundamental  tone. 

Overtones     .     .     i.      528  704 

.     .     2.      792  1,056 

.     .     3.  1,056  1,408 

.     .     4.  1,320  1,760 

.     .     5.  1,584  2,112 

Here  we  have  a  series  of  differences  each  equal  to  88,  but 
none  lower.  This  number,  though  within  the  vanishing 
limits  of  the  beats,  is  still  so  high  as  to  allow  very  little 
roughness.  Still  the  interval  is  clearly  inferior  to  the 
fifth. 

Again,  let  us  take  the  major  third.     Here  we  have  — 


SOUND.  49 

4  :         5 

Fundamental  tone        264  330     Fundamental  tone. 

Overtones     .     .     i.      528  660 

.     .     2.      792  990 

.     .     3.  1,056  1,320 

"  .     .     4.  1,320  1,650 

.     .     5.  1,584  1,980 

There  are  here  several  differences,  each  equal  to  66.     The 
beats  are  nearer  the  maximum  dissonance  than  in  the  last 
case,  and  the  consonance,  therefore,  is  less  perfect. 
We  will  now  try  the  minor  third.     Here  we  have  — 

5  ':        6 

Fundamental  tone         264  316.8    Fundamental  tone. 

Overtones     .     .     i.      528  633.6 

"                 .      .  2.  792  950.4 

"                •••:>>  3.  1,056  1,267.2 

"                 .      ;  4.  1,320  1,584.0 

.      .  5.  1,584  1,900.8 

Between  several  pairs  of  these  tones  we  have  a  differ- 
ence of  53  vibrations.  This  difference  implies  a  greater 
disturbance  by  beats  than  in  the  case  of  the  fifth,  or  of  the 
fourth,  or  of  the  major  third.  Hence  the  minor  third  is 
inferior  as  a  consonance  to  all  those  intervals. 

Thus  do  we  find  that,  as  the  numbers  expressing  the 
ratio  of  the  vibrations  become  larger,  the  disturbing  influ- 
ence of  the  beats  enters  more  and  more  into  the  interval. 
The  result,  it  is  manifest,  entirely  harmonizes  with  the 
explanation  that  refers  dissonance  to  beats. 

42.  The  Musical  Scale.  —  In  choosing  a  series  of  sounds 
for  combination  two  by  two,  the  simplicity  alone  of  the 
ratios  would  lead  us  to  fix  on  those  expressed  by  the  num- 
bers i,  £,  |,  f ,  -|,  2  ;  these  being  the  simplest  ratios  that 
we  can  have  within  an  octave.  But  when  the  notes  repre- 
3  D 


50  SOUND. 

sented  by  these  ratios  are  sounded  in  succession,  it  is 
found  that  the  intervals  between  i  and  J,  and  between  j 
and  2  are  wider  than  the  others,  and  require  the  inser- 
tion of  a  note  in  each  case.  The  notes  chosen  are  such 
as  form  chords,  not  with  the  fundamental  tone,  but  with 
the  note  f  regarded  as  a  fundamental  tone.  The  ratios  of 
these  two  notes  with  the  fundamental  are  f  and  V5-  In- 
serting  these,  we  have  the  eight  notes  of  the  natural  or 
diatonic  scale  expressed  by  the  following  names  and 
ratios  :  — 

Names.       C.     D.     E.     F.     G.     A.     B.     C'. 

Intervals,   ist.   2d.    3d.  4th.  5th.  6th.  ;th.  8th. 

Rates  of  vibration.      i,    |,      J»,      |,     |,     f,     ^-,     2. 

Multiplying  these  ratios  by  24  to  avoid  fractions,  we  ob- 
tain the  following  series  of  whole  numbers,  which  express 
the  relative  rates  of  vibration  of  the  notes  of  the  diatonic 
scale. 

24,  27,  30,  32,  36,  40,  45,  48. 

The  meaning  of  the  terms  third,  fourth,  fifth,  &c.,  which 
we  have  already  so  often  applied  to  the  musical  intervals, 
is  now  apparent ;  the  term  has  reference  to  the  position  of 
the  note  in  the  scale. 

SUMMARY. 

When  the  combination  of  two  notes  is  agreeable,  they  are 
said  to  form  a  chord;  when  their  combination  is  disagree- 
able, a  discord. 

The  simpler  the  ratio  of  the  vibrations  of  two  notes, 
the  more  agreeable  the  chord  which  they  form.  (40.) 

Dissonance  is  due  to  beats. 

It  is  greatest  when  the  beats  occur  at  the  rate  of  33  a 
second,  and  wholly  disappears  when  they  occur  at  the  rate 
of  132  a  second.  (41.) 


SOUND.  . 


MUSICAL   INSTRUMENTS. 

TRANSVERSE  VIBRATION  OF  STRINGS  AND  STRINGED 
INSTRUMENTS. 

43.  In  many  musical  instruments  the  sounds  are  pro- 
duced by  the  vibrations  of  strings  or  wires.  These  are 
called  stringed  instruments. 

We   proceed   now  to   examine   the   laws   according   to 


Fig.  30. 


which  strings  vibrate. 

44.  A  String  vibrating  alone 
gives  a  very  feeble  Sound.  —  In 
Figure  30  AB  is  a  wooden  bar 
placed  across  an  iron  bracket 
C.     mn  is  an  iron   bar  hung 
from  AB  by  means  of  ropes ; 
and  s  /  is  a  steel  wire  which  is 
stretched  by  a  weight.     If  we 
take  hold  of  the  middle  of  the 
string,  pull  it  to  one  side  and 
let  it  go  again,  its  elasticity  will 
cause   it   to   vibrate,   but    the 
sound  it  gives  out  can  scarcely 
be  heard. 

If  a  similar  string  stretched 
by  an  equal  weight  be  hung 
from  a  sounding-box  AB  (Fig- 
ure 31),  and  be  set  vibrating, 
the  sound  is  heard  distinctly. 

45.  Sounding-Boards. — From 
these  experiments  we  see  that 

some  kind  of  a  sounding-board  is  necessary  in  all  stringed 
instruments. 

It  is  not  the  chords  of  a  piano,  or  harp,  or  violin,  that 
throw  the  air  into  sonorous  vibrations.     It  is  the  large  sur- 


SOUND. 


Fig.  31- 


faces  connected  with  the  strings,  and  the  air  enclosed  by 

these  surfaces.  The 
merit  of  such  instru- 
ments depends  mainly 
upon  the  quality  and 
arrangement  of  their 
sounding-boards. 

The  violin,  for  ex- 
ample, is  made  of  wood 
of  the  most  perfect 
elasticity.  The  strings 
pass  from  the  tail- 
piece of  the  instru- 
ment over  the  bridge 
to  the  pegs  by  which 
they  are  tightened. 
The  two  feet  of  the 
bridge  rest  upon  the 
most  yielding  part  of 
the  body  of  the  violin  ; 
that  is,  the  portion  be- 
tween the  two^shaped  openings.  One  foot  is  fixed  over  a 
short  rod,  the  sound-post,  which  extends  across  to  the  back 
of  the  instrument.  This  foot  is  thereby  made  stiff,  and  it 
is  mainly  through  the  other  foot,  which  is  not  thus  sup- 
ported, that  the  vibrations  of  the  strings  are  conveyed  to 
the  wood  and  thence  to  the  air  within  and  without. 

The  sonorous  quality  of  the  wood  is  mellowed  by  the 
molecular  changes  which  take  place  with  the  lapse  of  time. 
The  very  act  of  playing,  too,  appears  to  make  the  mole- 
cules of  the  wood  conform  more  readily  to  the  vibrations 
of  the  strings,  and  thus  improves  the  instrument. 

46.  Laws  of  the  Vibration  of  Strings.  — The  laws  of  the 
vibration  of  strings  are  best  investigated  with  the  sonome- 
ter, which  has  already  been  described.  The  first  law  has 


SOUND. 


53 


already  been  found,  and  is  stated  thus  :   The  rapidity  of  the 
vibrations  is  inversely  as  the  length  of  the  string. 

47.  The  Rapidity  with  which  a  String  vibrates  varies  as 
the  Square  Root  of  the  Weight  which  stretches  it.  —  If  the 
string  B  B>  (Figure  32)  be  stretched  with  a  weight  of  one 
pound  and  made  to  vibrate,  a  note  of  a  certain  pitch  is  ob- 

Fig.  32. 


tained.  If  the  weight  be  made  four  pounds,  the  pitch  will 
be  raised  an  octave  ;  if  sixteen  pounds,  it  will  be  raised 
another  octave;  and  so  on.  The  rapidity  of  the  vibra- 
tions, then,  varies  as  the  square  root  of  the  weight  by 
which  the  string  is  stretched. 

48.  The  Rapidity  with  which  a   String  vibrates  varies 
inversely  as  its  Thickness.  —  If  strings  of  the  same  material 
but  of  different  thickness  be  stretched  over  the  bridges  by 
equal  weights,  the  thicker  strings  will  be  found  to  give  the 
lower  notes.     If  one  string  is  just  twice  as  thick  as  an- 
other, its  note  will  be  an  octave  lower.     In  general,  then, 
other  things  being  equal,  the  rapidity  of  the  vibrations  of  a 
string  varies  inversely  as  its  thickness. 

49.  The  Rapidity  with  which  a  String  vibrates  is  inversely 
as  the  Square  Root  of  its  Density.  —  It  is  found  that  if  a  plat- 


54  SOUND. 

mum  and  an  iron  wire  of  the  same  length  and  thickness 
be  stretched  by  equal  weights,  they  will  not  give  notes  of 
the  same  pitch.  The  greater  the  density  of  the  string,  the 
lower  the  pitch  of  the  note  which  it  gives.  It  is  found  on 
trial  that  the  pitch  of  the  sound  rises  as  the  square  root  of 
the  density  diminishes. 

The  last  two  laws  taken  together  may  be  stated  thus  : 
The  rapidity  with  which  strings  vibrate  is  inversely  propor- 
tional to  the  square  root  of  their  weight. 

In  one  class  of  stringed  instruments,  like  the  violin, 
violoncello,  and  guitar,  notes  of  a  great  variety  of  pitch  are 
obtained  from  a  few  strings  by  fingering  the  strings  so  as 
to  change  their  length.  In  another  class,  like  the  harp  and 
piano-forte,  many  strings  are  used  varying  in  length  and 
thickness,  each  of  which  gives  but  one  note. 

SUMMARY. 

Musical  sounds  may  be  produced  by  the  transverse  vi- 
brations of  strings.  (43.) 

The  sound  of  a  vibrating  string  must,  however,  be  en- 
forced by  a  sounding-board,  in  order  to  become  audible. 

(44,  45-) 

The  sonometer  is  an  instrument  for  investigating  the 
laws  of  vibrating  strings.  (46.) 

These  laws  are  three  in  number  :  — 

(i.)  The  rapidity  with  which  a  string  vibrates  varies 
inversely  as  its  length.  (46.) 

(2.)  The  rapidity  with  which  a  string  vibrates  varies  as 
the  square  root  of  the  weight  which  stretches  it.  (47.) 

(3.)  The  rapidity  with  which  a  string  vibrates  is  inversely 
as  the  square  root  of  its  weight.  (48,  49.) 

In  some  stringed  instruments  many  notes  are  produced 
by  few  strings  ;  in  others,  there  are  as  many  strings  as 
there  are  notes  given.  (49.) 


SOUND.  55 


LONGITUDINAL  VIBRATION  OF  STRINGS,  RODS,  AND 
COLUMNS  OF  AIR;   AND  WIND  INSTRUMENTS. 

50.  The  vibrations  of  strings  which  we  have   studied 
thus  far  take  place  at  right  angles  to  the  length  of  the 
string.     A  string  may  also  vibrate  in  the  direction  of  its 
length.     This  may  be  shown  by  drawing  a  piece  of  resined 
leather  along  the  wire  of  a  sonometer.     It  will  be  noticed 
that  the  sound  is  much  shriller  than  when  the  same  wire  is 
made  to  vibrate  transversely.      In  this  case  it  is  the  elastic 
force  acting  among  the  molecules  of  the  wire  which  causes 
it  to  vibrate ;   and,  owing  to  the  intensity  of  this  elastic 
force,  the  vibrations  are  much  more  rapid  than  in  the  other 
case. 

51.  The  shorter  the  Wire,  the  more  rapid  are  its  Longitu- 
dinal Vibrations.  —  Let  one  end  of  a  long  iron   wire  be 
firmly  fastened  to  a  fixed  wooden  sounding-box,  and  the 
other  end  wound  round  a  peg,  which  may  be  turned  by  a 
key  so  as  to  stretch  the  wire  more  or  less.     Pass  a  piece 
of  resined  leather  to  and  fro  along  the  wire,  and  a  musical 
sound  is  heard.     Put  a  bridge  under  the  middle  of  the 
wire,  and  rub  one  of  its  halves.     The  sound  heard  is  the 
octave  of  that  heard  at  first,  showing  that  the  vibrations 
are  twice  as  rapid.     Place  the  bridge  so  as  to  cut  off  one 
fourth  of  the  wire,  and  rub  that  fourth.     The  sound  pro- 
duced is  the  octave  of  the  last,  showing  that  the  vibrations 
are  four  times  as  rapid  as  at  first. 

We  see,  then,  that  the  shorter  the  wire  the  more  rapid 
its  longitudinal  vibrations. 

52.  The  Rapidity  of  the  Longitudinal  Vibrations  is  inde- 
pendent of  the  Tension  of  the  String.  —  Remove  the  bridge, 
so   that  the  iron  wire  may  vibrate  throughout  its  entire 
length.     Turn   the   key  so    as   to  change  the  tension   of 
the  wire,  and  again  rub  it.     The  pitch  of  the  note  does 


56  SOUND. 

not  change,  showing  that  the  rapidity  of  the  longitu- 
dinal vibrations  is  independent  of  the  tension  of  the 
wire. 

53.  How  to  find  the  Comparative  Velocity  of  Sound  in  Wires 
of  Different  Materials.  —  If  a  brass  wire  and  an  iron  wire  of 
the  same  length  and  thickness  be  made  to  vibrate  longitu- 
dinally, their  tones  are  not  the  same, — that  of  the  iron  wire 
being  considerably  the  higher  of  the  two.     In  the  case  of 
these  wires  the  sound  is  not  produced  by  the  wire  itself, 
but  by  the  sounding-box.     As  the  wire  vibrates  longitudi- 
nally, its  end  alternately  pushes  and  pulls  upon  the  sound- 
ing-box, and  thus  throws  the  air  within  it  into  vibrations. 
This  pushing  and  pulling  is  due  to  the  passage  of  the 
sound-pulse  to  and  fro  along  the  whole  wire.     The  time 
taken  by  the  pulse  in  running  the  length  of  the  wire  and 
back  is  that  of  a  complete  vibration  of  the  wire.     In  this 
time  the  wire  gives  one  pull  and  one  push  to  the  box  at  its 
end,  and  one  vibration  to  the  air  within  it.     The  faster  the 
pulse  passes  along  the  wire,  the  higher  the  note  produced. 
If  the  brass  wire  be  shortened  until  it  gives  a  note  of  the 
same  pitch  as  that  given  by  the  iron  wire,  it  is  evident  that 
the  sound-pulse  traverses  each  of  the  wires  in  the  same 
time.     The  length  of  the  wires  will  be  found  to  be  in  the 
ratio  of  n  to  17,  showing  that  sound  travels  only  ^  as  fast 
in  brass  as  in  iron. 

54.  The  Longitudinal  Vibrations  of  Rods  free  at  one  End. 
—  A  smooth  wooden  or  metallic  rod  with  one  of  its  ends 
fixed  in  a  vise  yields  a  musical  note  when   rubbed  with 
resined  leather.     When  a  rod  fastened  in  this  way  yields 
its  fundamental  note  (29),  it  simply  lengthens  and  short- 
ens in  quick  succession.     When  rods  of  different  lengths 
are  compared,  the  pitch  of  the  note  is  found  to  increase  as 
the  length  diminishes.     By  taking  advantage  of  this  fact, 
a  musical    instrument   has  been  constructed,   such   as  is 
shown    in   Figure  33,   which   produces  notes  of  different 


SOUND. 


57 


pitch  by  the   longitudinal  vibrations  of  wooden    rods   of 
different  lengths.  Fig.  33. 

55.  Longitudinal  Vibrations  of 
Rods  free  at  both  Ends,  —  Clasp  a 
long  glass  tube  at  its  centre  with 
one  hand,  and  rub  a  wet  cloth  over 
one  of  its  halves  with  the  other. 
A  musical  sound  is  produced.  A 
solid  glass  rod  of  the  same  length 
will  give  the  same  note.  In  this 
case  the  centre  of  the  tube  or  rod  is 
a  node,  and  the  two  halves  lengthen 
and  shorten  in  quick  succession. 
This  lengthening  and  shorten- 
ing of  the  halves  of  the  rod  is  shown  by  the  apparatus 
represented  in  Figure  34.  a  b  is  a  brass  rod  held  at 
its  centre  by  the  clamp  s ;  and  an  ivory  ball  hung  by  two 
strings  from  the  points  m  and  n  rests  against  the  end  b  of 

Fig.  34- 


the  rod.  On  drawing  a  piece  of  resined  leather  gently 
over  the  rod  near  #,  it  is  thrown  into  longitudinal  vibra- 
tions. The  centre  s  is  at  rest,  but  the  motion  of  the  ivory 
ball  shows  that  the  end  b  is  in  a  state  of  tremor.  Rub  the 
rod  more  briskly,  and  its  vibrations  become  more  intense. 

a* 


SOUND. 


Fig.  35- 


and    the   ivory  ball    is  thrown    off  violently  whenever  it 
comes  in  contact  with  the  end  of  the  rod. 

If  a  long  glass  tube  be  held  at  the  centre,  and  one  half 
of  it  be  rubbed  briskly  with  a  wet  cloth,  the  strain  upon 
the  glass  caused  by  the  longitudinal  vibrations  may  be 
sufficient  to  shiver  the  other  end,  as  shown  in  Figure  35. 

56.  How  to  find  the  Velocity  of  Sound 
in -different  Solids.  —  In  all  cases  the 
longitudinal  vibrations  of  rods  are  pro- 
duced by  the  passage  of  the  sound- 
pulse  to  and  fro  along  them.  The 
pitch  of  the  note  given  by  rods  of  the 
same  length  depends  upon  the  rapidity 
with  which  the  pulse  passes.  The  ve- 
locity of  sound  in  different  solids  can 
be  compared  by  means  of  rods  free  at 
both  ends,  as  well  as  by  means  of  wires. 
We  -have  only  to  take  rods  of  the  dif- 
ferent solids,  of  such  lengths  that  they 
will  give  notes  of  the  same  pitch,  and 
these  lengths  will  be  in  the  inverse  ratio 
of  the  velocities  required. 

57-  Resonance. — When  a  tuning-fork 
is  detached  from  the  sounding-box 
and  made  to  vibrate,  it  can  hardly  be  heard.  Let,  now, 
the  fork  be  held  over  a  glass  jar  A  B  (Figure  36) 
some  1 8  inches  deep,  and  the  sound  is  still  very  faint 
Keep  the  fork  in  this  position,  and  pour  water  with  the 
least  possible  noise  into  the  jar.  As  the  column  of  air 
under  the  fork  becomes  shorter,  the  sound  becomes 
louder ;  and  when  the  water  has  reached  a  certain  level,  it 
bursts  forth  with  great  power.  Continue  to  pour  water 
into  the  jar,  and  the  sound  becomes  weaker  and  weaker, 
until  it  is  as  faint  as  at  first.  Pour  the  water  carefully  out, 
and  we  reach  a  point  where  the  sound  is  reinforced  again. 


SOUND. 


59 


In  this  way  we  find  that  there  is  one  particular  length  of 
the  column  of\air  which  causes  the  fork  above  it  to  give 

Fig.  36. 


Fig.  37. 


384 


the  loudest  possible  sound.     This  reinforcement  of  sound 
is  called  resonance. 

By  trying  tuning-forks  of 
different  pitch,  we  find  in 
this  way  a  column  of  air 
for  each  which  gives  the 
greatest  resonance.  These 
columns  are  of  different 
lengths,  becoming  shorter 
as  the  forks  vibrate  faster. 

Figure  37  shows  the  rela- 
tive lengths  of  jars  which 
give  the  greatest  resonance 

for  tuning-forks  vibrating  256,  320,  384,  and  512  times  in 
a  second. 


512 


6o 


SOUND. 


58.  The  Length  of  the  Column  of  Air  which  resounds  to 
a  vibrating  Fork  is  equal  to  one  fourth  the  Length  of  the 
Wave  produced  by  the  Fork. — The  greater  volume  of  sound 
when  the  fork  is  vibrating  over  a  resonant  jar  can  be  due 
only  to  the  greater  amount  of  motion  communicated  to  the 
air.  When  is  the  fork  enabled  thus  to  increase  the  mo- 
tion ? 

We  have  seen  that  a  fork  vibrating  256  times  a  second 
produces  a  sound-wave  4  feet  4  inches  long  (23).  In  Fig- 
ure 38,  suppose  a  prong  of  the  fork  to  be  vibrating  between 


a    b 


V 


Fig.  38. 

20  inches 


' 


the  points  a  and  b.  In  going  from  a  to  b,  the  prong  gen- 
erates half  a  sound-wave  ;  and  when  it  reaches  bt  the  fore- 
most point  of  the  wave  will  be  at 
c,  2  feet  2  inches  from  the  fork. 

<What  then  is  the  length  of  the 
,-—---- a       column  of  air  which  resounds  most 

powerfully  for  this  fork  ?  By 
measurement  we  find  it  to  be  13 
inches.  But  the  whole  length  of 
the  sound-wave  produced  by  the 
fork  is  52  inches.  Hence  the 
length  of  the  column  of  air  which 
resounds  for  this  fork  is  one  fourth 
the  length  of  the  sound-wave  pro- 
duced by  the  fork.  We  find  the 
same  to  be  true  in  the  case  of  every  fork. 


SOUND.  6 1 

59.  Cause  of  Resonance.  —  Suppose  now  the  prong  of 
the  fork  to  be  vibrating  over  the  jar  A  B  (Figure  39). 
While  the  prong  is  moving  from  a  to  b,  the  compression 
which  it  produces  runs  to  the  bottom  of  the  jar,  where  it  is 
reflected ;  and  as  the  distance  down  and  back  is  26  inches, 
the  reflected  wave  will  reach  the  fork  just  as  it  is  on  the 
point  of  returning  from  b  to  a.     The  extension  of  the  wave 
is  caused  by  the  retreat  of  the  prong  from  b  to  a,  and  will 
also  run  to  the  bottom  of  the  jar  and  back  in  time  to  over- 
take the  prong  just  as  it  reaches  the  point  a.     If  now  the 
prong  were  to  remain  at  a,  the  molecules  of  air  on  reach- 
ing it  would  rebound,  and  thus  produce  a  compression  of 
the  air  in  the  jar  ;  but  just  as  they  are  ready  to  rebound, 
the  prong  begins  to  move  downward,  and  gives  them  a 
push.     Now,  as  this  push  is  given  every  time  just  as  they 
are  about  to   rebound,  it  adds  more  and  more  to  their 
motion  ;  much  in  the  same  way  as  a  heavy  ball  hung  by  a 
string  may  be  made  to  swing  through  a  great  distance  by 
a  succession  of  very  slight  pushes,  provided  they  are  so 
timed  as  to  act  upon  the  ball  just  as  it  is  ready  to  retreat. 
If  the  pushes  are  not  thus  timed,  they  are  as  likely  to 
check  the  motion  as  to  increase  it.     So  in  the  case  of  the 
resonant  jar ;  the  vibrations  of  the  column  of  air  would  be 
as  likely  to  be  checked  as  increased,  if  they  were  not  syn- 
chronous with  those  of  the  fork.     It  is  thus  seen  that  the 
vibrations  of  the  fork  are  perfectly  synchronous  with  (that 
is,  take  place  in  the  same  time  with)  those  of  the  column 
of  air  A  B. 

60.  Savarfs  Illustration  of  Resonance.  —  If  a   bow  be 
drawn  across  the  edge  of  a  bell  (Figure  40),  it  gives  out 
a  musical  sound.     If  now  the  open  mouth  of  a  cylinder 
closed  at  the  other  end  be  brought  near  one  of  the  vibrat- 
ing parts  of  the  bell,  the  sound  is  greatly  reinforced.     If 
the  cylinder  be  alternately  removed  and  brought  near,  the 
sound  sinks  and  swells  in  a  striking  manner.     If  it  be 


62  SOUND. 

allowed  to  sink  until  it  cannot  be  heard,  and  the  cylinder 
be  again  brought  near,  the  sound  becomes  audible  again; 

Fig.  40. 


6 1.  Further  Facts  concerning  Resonance.  —  "The  reso- 
nance of  caves  and  of  rocky  enclosures  is  well  known. 
Bunsen  notices  the  thunder-like  sound  produced  when  one 
of  the  steam  jets  of  Iceland  breaks  out  near  the  mouth  of 
a  cavern.  Most  travellers  in  Switzerland  have  noticed  the 
deafening  sound  produced  by  the  fall  of  the  Reuss  at  the 
Devil's  Bridge.  The  noise  of  the  fall  is  raised  by  reso- 
nance to  the  intensity  of  .thunder.  The  sound  heard  when 
a  hollow  shell  is  placed  close  to  the  ear  is  a  case  of  reso- 
nance. Children  think  they  hear  in  it  the  sound  of  the 
sea.  The  noise  is  really  due  to  the  reinforcement  of  the 
feeble  sounds  with  which  even  the  stillest  air  is  pervaded. 
By  using  tubes  of  different  lengths,  the  variation  of  the 
resonance  with  the  length  of  the  tube  may  be  noticed. 
The  channel  of  the  ear  itself  is  also  a  resonant  cavity. 
When  a  poker  is  held  by  two  strings,  and  when  the  fingers 
of  the  hands  holding  the  poker  are  thrust  into  the  ears,  on 
striking  the  poker  against  a  piece  of  wood  a  sound  is 


SOUND.  63 

heard  as  deep  and  sonorous  as  that  of  a  cathedral  bell. 
When  open,  the  channel  of  the  ear  resounds  to  notes 
whose  periods  of  vibration  are  about  3,000  per  second. 
This  has  been  shown  by  Helmholtz  ;  and  a  German  lady 
named  Seiler  has  found  that  dogs  which  howl  to  music  are 
particularly  sensitive  to  the  same  notes."  (Tyndall.) 

62.  A  Column  of  Air  may  be  made  to  vibrate  by  blowing 
across  the  End  of  a  Tube.  —  Select  two  jars,  and  two  tuning- 
forks  which  will  cause  them  to  resound.  Cause  both  forks 
to  vibrate,  and  hold  them  both  over  one  of  the  jars.  Only 
one  of  them  is  heard.  Hold  them  both  over  the  other  jar, 
and  the  other  fork  alone  is  heard.  Each  jar  selects  that 
fork  for  reinforcement  whose  vibrations  are  synchronous 
with  its  own.  Instead  of  two  forks,  two  dozen  might  be 
held  over  either  of  these  jars,  and  from  the  medley  of 
pulses  thus  generated  the  jar  would  select  and  reinforce 
the  one  which  corresponds  to  its  own  period  of  vibration. 

Blow  now  across  the  open  mouth  of  this  same  jar,  or 
across  the  mouth  of  a  glass  tube  of  the  same  length  as 
the  jar,  and  J  of  an  inch  in  diameter  (Figure 
41).  A  fluttering  of  the  air  is  thus  produced  ; 
in  fact,  a  medley  of  pulses  is  generated  at  the 
mouth  of  the  tube.  The  tube  selects  the  pulse 
which  is  synchronous  with  its  own  vibration, 
and  reinforces  it  so  that  it  becomes  a  musical 
sound.  The  sound  is  the  same  as  that  pro- 
duced by  the  proper  tuning-fork  held  over  the 
tube.  The  column  of  air  in  the  tube  has,  in 
fact,  made  its  own  tuning-fork ;  for,  by  the  re- 
action of  its  pulses,  it  has  made  the  air  blown 
across  the  tube  vibrate  in  unison  with  itself. 

On  blowing  across  the  mouth  of  a  tube  of 
any  length,  a  musical  sound  is  produced  exactly 
like  that  obtained  when  the  proper  tuning-fork  is  held  ov 
the  tube. 


64  SOUND. 

63.  The  Rate  of  Vibration  of  a  Column  of  Air  in  a  Tube 
is  inversely  proportional  to  its  Length.  —  Take  three  tubes 
6,  12,  and  24  inches  long.     Blow  gently  across  the  mouth 
of  each  tube  so  as  to  bring  out  its  fundamental  note.    The 
note  of  the  1 2-inch  tube  will  be  the  octave  of  the  note  of 
the  24-inch  tube,  and  that  of  the  6-inch  tube  the  octave 
of  that  of  the  1 2-inch  tube.     This  must  be  the  case  ;  for, 
since  the  rate  of  vibration  depends  upon  the  distance  the 
pulse  must  travel  to  complete  a  vibration,  the  greater  this 
distance  the  slower  the  vibration.     In  other  words,  the  rate 
of  vibration  is  inversely  proportional  to  the  length  of  the 
tube  through  which  the  pulse  passes. 

64.  Vibrations  in  Open  Tubes.  —  The  tubes  which  have 
been  used  thus  far  have  been  closed  at  one  end.     Such 
tubes  are  called  stopped  tubes.     We  will  next  examine  the 
vibrations  of  tubes  open  at  both  ends,  or  open  tubes.     If 
we  take  a  stopped  tube  and  an  open  tube  of  the  same 
length,  and  blow  gently  across  the  mouth  of  each  so  as  to 
get  its  fundamental  note,  we  shall  find  the  note  of  the 
latter  an  octave  higher  than  that  of  the  former.     An  open 
tube   always   yields   the   octave   of  the  note  given  by  a 
stopped  tube  of  the  same  length. 

65.  Organ-Pipes. — Organ-pipes  are  nothing  more  than 
resonant  tubes.     There  are  various  ways  of  agitating  the 
air  at  the  mouth  of  such  tubes,  so  as  to  set  the  columns 
of  air  within  them  into  vibrations.     In  one  kind  of  organ- 
pipes,  this  is  done  by  blowing  a  thin  sheet  of  air  against  a 
sharp  edge.     This  produces  a  flutter,  some  particular  pulse 
of  which  is  then  converted  into  a  musical  sound  by  the 
resonance  of  the  air  in  the  tube. 

Figure  42  represents  an  open  organ-pipe'.  The  air 
passes  from  the  bellows  through  the  tube  P  into  a  cham- 
ber, which  is  closed  at  the  top  except  the  narrow  slit  i. 
The  air  compressed  in  the  chamber  passes  through  this  slit 
in  a  thin  sheet  which  breaks  against  the  sharp  edge  a,  and 


SOUND. 


there  produces  a  flutter.     The  space  between  the  ^dge  a 
and  the  slit  below  is  called  the  mouth  of  the  pipe. 


Fig.  42. 


Fig.  43- 


Figure  43  represents  a  stopped  organ-pipe,  so  called  be- 
cause its  upper  end  is  closed.  Instead  of  producing  a 
flutter  at  the  mouth  of  the  pipe  by  a  blast  of  air,  we  may 
get  the  same  effect  by  holding  at  the  mouth  of  the  pipe 
(Figure  44)  a  tuning-fork  whose  vibrations  are  synchronous 
with  those  of  the  pipe.  Select  several  pipes  of  different 
lengths,  and  tuning-forks  which  vibrate  in  unison  with 
each.  Beginning  with  the  longest  pipe,  make  the  fork  of 
lowest  pitch  vibrate  near  its  mouth.  The  pipe  speaks  pow- 
erfully. Blow  into  the  same  pipe  ;  its  tone  is  exactly  the 
same  as  when  the  fork  was  held  at  its  mouth.  Try  each 

E 


66 


SOUND. 


of  the  pipes  in  the  same  way,  and  the  note  which  each 
gives  when  blown  into  is  exactly  that  given  when  the 
proper  fork  is  at  its  mouth.  If  all  the  forks  are  held  at 
the  same  time  at  the  mouth  of  any  one  of  the  pipes,  their 
vibrations  will  produce  pulses  of  very  different  period. 
Out  of  all  these,  however,  the  pipe  will  select  and  reinforce 
but  one.  The  result  would  be  the  same  if  several  hun- 
dred forks  of  different  pitch  were  vibrating  at  the  mouth 

Fig.  45- 


of  the  pipe.  So  also  the  current  of  air 
striking  against  the  sharp  upper  edge  of 
the  mouth  of  the  pipe  gives  rise  to  a 
great  variety  of  pulses,  from  which  the 
pipe  selects  and  reinforces  but  one. 

66.   The  Condition  of  the  Air  within 
an  Organ-Pipe  examined  by  means  of  a 
Membrane.  —  The  front  of  the  organ- 
pipe  in  Figure  45  is  of  glass,  so  that  we  can  see  the  posi- 
tion of  any  body  within.      If  now  the  pipe  be  made  to 


SOUND.  67 

speak,  and  a  thin  membrane  stretched  upon  a  light  frame 
be  let  down  into  it  by  a  string,  on  entering  the  pipe  the 
membrane  begins  to  give  a  rattling  sound.  This  continues 
until  it  reaches  the  centre,  when  it  ceases  to  sound.  On 
passing  below  the  centre,  it  again  begins  to  rattle.  It  is 
made  to  rattle  above  and  below  the  centre  by  means  of  the 
particles  of  air  which  are  there  vibrating  against  it.  The 
fact  that  it  is  silent  at  the  centre  of  the  pipe  shows  that 
the  particles  of  air  are  there  at  rest.  The  centre  of  the 
column  of  air  in  the  open  pipe  is  then  a  node.  Such  a 
column  of  air  vibrates  like  a  rod  free  at  both  ends  (55). 
There  is  no  vibration  at  the  centre,  but  alternate  compres- 
sion and  extension,  while  at  the  ends  there  is  little  change 
of  density  but  the  maximum  of  vibration. 

67.  The  Condition  of  the  Air  in  an  Organ-Pipe  examined 
by  means  of  Gas-jets.  —  If  a  sounding  pipe  were  pierced  at 
the  centre,  and  the  hole  stopped  by  an  elastic  membrane, 
the  air  when  compressed  at  this  point  would  push  the 
membrane  outward.  On  the  other  hand,  when  the  air 
within  was  extended,  the  outer  air  would  press  the  mem- 
brane inward.  The  membrane  would  thus  be  made  to 
vibrate  in  unison  with  the  column  of  air.  If  holes  were 
made  near  the  ends  of  the  pipe  and  stopped  in  a  similar 
manner,  the  membranes  would  not  vibrate,  since  the  air  at 
these  points  is  not  undergoing  changes  of  density. 

By  means  then  of  a  pipe  pierced  in  this  way  we  can 
ascertain  experimentally  whether  the  air  within  the  pipe 
is  undergoing  changes  of  density  at  the  centre  and  not 
at  the  ends.  Figure  46  represents  a  pipe  arranged  for 
this  experiment.  The  pipe  is  pierced  at  the  points  A,  £, 
and  C,  and  the  holes  are  closed  by  elastic  membranes. 
Over  each  membrane  is  a  little  chamber  which  is  filled 
with  gas  by  means  of  the  pipe  S.  Projecting  from  each 
chamber  is  a  small  bent  burner.  Light  the  three  burners 
and  blow  into  the  pipe.  All  the  flames  are  agitated,  but 


68 


SOUND. 


the   centre   one    much    the    most.  F'l&-  *6- 

Turn    down    the   gas  so   that   the 

flames  may  be  very  small,  and  blow 

into  the  pipe  again.      The  centre 

flame  will  be  blown  out,  the  others 

will  still  burn.     It  is  evident,  then, 

that  the  membrane  at   the    centre 

vibrates  much  more  strongly  than 

the  others. 

68.  Why  an  Open  Pipe  gives  the 
Octave  of  a  Stopped  Pipe  of  the  same 
Length.  —  When  a  column  of  air  is 
vibrating  in  a  pipe  closed  at  one 
end,  the  closed  end  is  evidently  a 
node,  for  the  molecules  of  air  near 
it  have  no  chance  to  vibrate.     In 
the  case  of  an  open  pipe,  the  node 
is  at  the  centre,  and  the  parts  of 
the  air  vibrating  are  only  half  the 
length  of  the  pipe.     Hence    they 
will  vibrate  twice  as  rapidly  as  the 

column  of  air  in  the  stopped  pipe,  if  the  pipes  are  of  the 
same  length. 

69.  How  to  find  the  Relative  Velocity  of  Sound  in  Different 
Gases. — We  have  seen  (58)  that  the  length  of  a  resonant 
jar  is  one  fourth  that  of  the  sound-wave  which  it  produces  ; 
therefore  the  length  of  a  stopped  organ-pipe  will  be  one 
fourth  the  length  of  its  sound-wave,  and  the  length  of  an 
open  pipe  one  half  that  of  its  sound-wave. 

If  a  jar  which  resounds  to  a  tuning-fork  be  inverted  and 
filled  with  hydrogen,  it  will  no  longer  resound  to  this  fork  ; 
but  if  a  jar  four  times  as  long  be  filled  with  hydrogen,  it 
will  resound  to  this  fork.  But  the  sound-wave  must  run 
to  the  bottom  of  the  jar  and  back  while  the  fork  is  per- 
forming one  half  a  vibration  (59).  Hence  the  wave  must 
travel  four  times  as  fast  in  hydrogen  as  in  air. 


SOUND.  69 

Now  organ-pipes  can  be  made  to  speak  by  blowing  other 
gases  than  air  through  them,  and  we  can  accordingly  find 
the  relative  velocity  of  sound  in  different  gases  by  finding 
the  length  of  the  organ-pipe  which  must  be  used  with  each 
in  order  to  give  a  note  of  the  same  pitch. 

70.  How  to  find  the  Relative  Velocity  of  Sound  in  Different 
Liquids.  —  By  forcing  liquids  through  properly  constructed 
organ-pipes  they  may  be  made  to  speak,  just  as  when  gases 
are  forced  through  them.     By  using  different  liquids  and 
finding  a  series  of  pipes  which  give  the  same  note  with 
each,  we  can  determine  the  relative  velocity  of  sound  in 
those  liquids.     Thus,  if  a  solution  of  common  salt  is  forced 
through  one  pipe  and  alcohol  through  another,  it  will  be 
found  that  the  latter  pipe  must  be  about  three  times  as 
long  as  the  former,  in  order  to  give  the  same  note  ;  showing 
that  the  velocity  of  sound  in  alcohol  is  about  three  times 
as  great  as  in  a  solution  of  salt. 

7 1 .  How  to  find  the  Actual  Velocity  of  Sound  in  Different 
Substances. — We  have  now  learned  how  to  find  the  rela- 
tive velocity  of  sound  in  different  solids,  liquids,  a-nd  gases, 
and  the  actual  velocity  of  sound  in  air.     How  can  we  find 
its  actual  velocity  in  other  substances  than  air?     We  evi- 
dently can  find  its  velocity  in  other  gases  by  multiplying 
its  velocity  in  air  by  its  relative  velocity  in  the  gases.     To 
find  its  actual  velocity  in  liquids,  we  must  first  know  its 
velocity  in  some  one  liquid  compared  with  its  velocity  in 
air.     The  velocity  of  sound   in   water  may  be  compared 
with  its  velocity  in  air  by  forcing  water  and  air  through 
organ-pipes.     It  is  thus  found  that  water  requires  a  pipe  a 
little  more  than  four  feet  long  to  give  the  same  note  that 
air  will  give  in  a  pipe  one  foot  long;   showing  that  the 
velocity  of  sound  in  water  is  a  little  more  than  four  times 
its  velocity  in  air.    After  having  found  its  velocity  in  water, 
its  velocity  in  other  liquids  may  be  found  by  multiplying  its 
velocity  in  water  by  its  relative  velocity  in  these  liquids. 


70  SOUND. 

The  velocity  of  sound  in  any  solid,  as  pine  wood,  may 
be  compared  with  its  velocity  in  air  by  finding  the  length 
of  a  rod  of  pine  which  yields  the  same  note  as  an  organ- 
pipe.  It  is  thus  found  that  the  rod  must  be  ten  times  as 
long  as  the  pipe,  —  showing  that  the  velocity  of  sound  in 
pine  is  ten  times  its  velocity  in  air.  The  velocity  of  sound 
in  other  solids  may  be  found  by  multiplying  its  velocity  in 
pine  wood  by  its  relative  velocity  in  those  solids. 

72.  Reed  Pipes.  —  A  column  of  air  may  be  made  to 
vibrate  by  means  of  a  spring  of  metal  or  wood,  called  a 
reed.  The  metal  reed  commonly  used  in  organ-pipes  is 
shown  in  Figure  47.  It  consists  of  a  long  and  flexible 

Fig.  47- 


strip  of  metal,  V  V,  placed  in  a  rectangular  opening  through 
which  the  current  of  air  enters  the  pipe.  As  soon  as  the 
air  begins  to  enter  the  pipe,  the  force  of  the  blast  bends 
down  the  spring  of  the  reed  so  as  to  close  the  opening. 
The  elasticity  of  the  reed  causes  it  to  fly  back  at  once,  so 
as  to  open  the  pipe  and  allow  the  air  to  enter  again.  It 
thus  breaks  up  the  current  of  air  into  a  regular  succession 
of  little  puffs. 

The  way  in  which  the  reed  and  the  pipe  are  connected 
is  shown  in  Figure  48.  The  reed  is  placed  within  the 
chamber  A",  into  which  air  is  forced  through  the  tube  at  the 
bottom.  T  is  a  conical  pipe  of  metal,  the  opening  of  which 
is  covered  by  the  reed,  as  already  explained.  The  wire  b  r 


SOUND.  7 1 

is  used  to  lengthen  or  shorten  the  reed,  and  thus  to  vary 
its  rate  of  vibration. 

Fig.  48. 


When  the  vibrations  of  the  reed  and  the  pipe  are  ex- 
actly synchronous,  the  sound  is  most  pure  and  forcible.  If 
their  rates  of  vibration  vary  beyond  a  certain  limit,  the 
pipe  ceases  to  be  of  any  use,  and  the  reed  vibrates  alone. 
Unless,  however,  the  reed  is  quite  stiff,  the  column  of  air 
compels  it  to  vibrate  in  unison  with  itself.  This  may  be 
illustrated  by  means  of  a  common  straw.  With  a  pen- 
Fig.  49- 


knife  raise  a  strip  of  the  straw  near  a  knot,  as  shown  at  rr 
in  Figure  49.  This  strip  serves  as  a  reed,  and  the  straw  as 
a  pipe.  Blow  into  it,  and  it  gives  a  musical  note.  Make 


72  SOUND. 

it  shorter  and  shorter,  and  the  note  rises  higher  and  higher. 
Here  the  reed  remains  the  same,  but  is  compelled  to  make 
its  vibrations  synchronous  with  those  of  the  varying  column 
of  air. 

The  clarionet  is  a  reed  pipe.  It  has  a  single  broad 
tongue  at  the  mouth  of  a  long  cylindrical  tube.  By  the 
pressure  of  the  lips  the  slit  between  the  reed  and  its  frame 
is  narrowed  to  the  proper  extent.  The  different  notes  are 
obtained  partly  by  increasing  the  force  of  the  blast  so  as  to 
produce  overtones  (29),  and  partly  by  varying  the  length  of 
the  resonant  column  of  air  by  openings  in  the  sides  of  the 
tube. 

In  the  horn,  trumpet,  and  similar  instruments,  the  lips  of 
the  player  take  the  place  of  the  reed. 

73.  Two  Classes  of  Wind  Instruments.  — In  one  class  of 
wind  instruments,  as  the  flute  and  fife,  a  single  column  of 
air  is  made  to  give  a  great  number  of  notes.  In  this  case 
the  length  of  the  column  is  varied  at  pleasure  by  means  of 
keys.  In  another  class,  as  the  organ,  there  is  a  pipe  for 
every  note. 

SUMMARY. 

Wires  and  rods  may  vibrate  longitudinally  as  well  as 
transversely.  (50.) 

Longitudinal  vibrations  are  much  more  rapid  then  trans- 
verse vibrations,  and  increase  in  rapidity  as  the  rods  dimin- 
ish in  length.  (51.) 

These  vibrations  may  be  illustrated  by  means  of  rods 
free  at  one  end  or  at  both  ends,  (54,  55.) 

The  velocity  of  sound  in  different  solids  may  be  com- 
pared by  causing  rods  of  those  solids  to  vibrate  longitudi- 
nally. The  velocity  of  sound  in  different  solids  is  inversely 
proportional  to  the  length  of  the  rods  which  give  notes  of 
the  same  pitch.  (56.) 

The  sound  of  a  tuning-fork  is  reinforced  when  it  vibrates 


SOUND.  73 

over  the  mouth  of  a  jar  of  air  of  a  certain  depth.  The 
depth  of  the  jar  is  different  for  forks  of  different  pitch. 
This  reinforcement  of  sound  is  called  resonance.  (57.) 

The  length  of  a  column  of  air  which  reinforces  the  sound 
most  is  equal  to  one  fourth  the  length  of  the  wave  pro- 
duced by  the  fork.  (58.) 

The  vibrations  of  a  resonant  column  of  air  are  synchro- 
nous with  those  of  the  sounding  body.  It  is  this  syn- 
chronism which  causes  the  motion  of  the  particles  of  the 
air  to  accumulate  so  as  to  produce  the  resonance.  (59.) 

Jars  and  tubes  may  be  made  resonant  by  blowing  across 
their  open  mouths,  and  give  the  same  note  as  when  made 
to  resound  by  a  tuning-fork.  (62.) 

The  shorter  the  column  of  air,  the  faster  it  vibrates.    (63.) 

An  open  tube  gives  a  note  which  is  the  octave  of  a 
closed  tube  of  the  same  length.  (64.) 

Organ-pipes  are  resonant  tubes.  When  open  at  both 
ends,  they  are  called  open  pipes ;  when  closed  at  one  end, 
stopped  pipes. 

One  kind  of  organ-pipe  is  made  to  resound  by  blowing 
a  thin  sheet  of  air  against  a  sharp  edge  at  its  mouth. 

(65-) 

The  condition  of  the  air  within  an  organ-pipe  may  be 
examined  by  means  of  a  stretched  membrane,  or  by 
means  of  gas-jets. 

When  an  open  pipe  is  giving  its  fundamental  note,  the 
centre  is  a  node,  and  the  column  of  air  is  vibrating  in  the 
same  way  as  a  rod  free  at  both  ends.  At  the  centre  of  the 
column  there  is  the  minimum  of  vibration,  and  the  maxi- 
mum of  change  in  density  ;  while  at  the  ends  there  is  the 
maximum  of  vibration,  and  the  minimum  of  change  in 
density.  (66,  67.) 

In  a  stopped  pipe  the  end  is  a  node,  so  that  such  a  pipe 
is  equivalent  to  an  open  pipe  of  twice  the  length.  (68.) 

The  length  of  a  stopped  pipe  is  one  fourth  that  of  the 
4 


74 


SOUND. 


sound-wave  which  it  produces  ;  while  that  of  an  open  pipe 
is  one  half  that  of  the  sound-wave  it  produces. 

The  velocities  of  sound  in  different  gases,  liquids,  and 
solids  may  be  determined  from  the  lengths  of  these  sub- 
stances which  give  notes  of  the  same  pitch.  (69,  70,  71.) 

A  column  of  air  may  be  made  to  vibrate  by  means  of  a 
reed. 

When  the  reed  is  limber,  it  is  compelled  to  vibrate  in 
unison  with  the  column  of  air  in  the  pipe  with  which  it  is 
connected  ;  when  it  is  stiff,  its  rate  of  vibration  is  but  little 
affected  by  the  resonance  of  the  air  in  the  pipe. 

The  clarionet  and  many  other  wind  instruments  are 
reed-pipes.  (72.) 

There  are  two  classes  of  wind  instruments.     (73.) 


Fig.  50. 


SOUNDING   FLAMES. 

74.  Friction  always  Rhythmic.  — 
When  we  draw  a  bow  across  a  string, 
or  rub  a  wet  finger  round  the  edge 
of  a  glass,  a  musical  sound  is  pro- 
duced, showing  that  the  friction  has 
been  broken  up  into  rhythmic  pulses. 
Close  the  lower  end  of  the  tube  A  B 
(Figure  50)  with  a  metallic  plate, 
pierced  by  a  round  hole  whose  di- 
ameter is  equal  to  the  thickness  of 
the  plate.  Plug  the  hole,  and  fill 
the  tube  with  water.  Remove  the 
plug,  and,  as  the  water  sinks  in  the 
tube,  a  very  sweet  musical  note  is 
given  out  by  the  liquid  column. 
This  note  is  due  to  the  intermittent 
flow  of  the  water  through  the  hole, 
by  which  the  column  above  is  thrown 
into  vibrations.  The  same  intermit- 


SOUND.  75 

tence  is  observed  in  the  dense  smoke  which  rolls  in  rhyth- 
mic rings  from  the  funnel  of  a  steamboat.  The  noise  pro- 
duced by  the  friction  of  machinery  is  due  to  the  alternate 
"  bite  "  and  release  of  the  rubbing  surfaces. 

The  friction  of  gases  is  of  the  same  intermittent  charac- 
ter. A  rifle-ball  sings  as  it  passes  through  the  air.  "  The 
whispering  pines  "  owe  their  music  to  the  rubbing  of  the 
wind  against  their  branches  and  foliage.  The  whistling  of 
the  wind  is  also  produced  by  the  rhythmic  friction  of  the 
air. 

If  we  blow  gently  against  a  candle-flame,  the  fluttering 
noise  announces  a  rhythmic  action.  We  have  already 
learned  (65)  that,  when  a  pipe  is  associated  with  a  flutter, 
it  selects  from  it  a  special  pulse,  and  raises  it  by  resonance 
to  a  musical  sound.  In  like  manner,  the  noise  of  a  flame 
may  be  converted  into  a  musical  note.  The  special  pulse 
first  selected  soon  reacts  upon  the  flame  so  as  to  destroy, 
in  a  great  degree,  the  other  pulses,  and  compels  the  flame 
to  vibrate  in  unison  with  itself. 

When  a  gas-flame  is  simply  enclosed  in  a  tube,  the  pas- 
sage of  the  air  over  it  is  usually  sufficient  to  produce  the 
necessary  rhythmic  action,  and  to  make  it  sing.  With  a 
tube  15  feet  long  and  4  inches  wide,  and  a  large  Bunsen's 
burner,  Professor  Tyndall  produced  a  sound  powerful 
enough  to  shake  the  floor  and  seats,  and  the  large  audi- 
ence that  occupied  the  seats,  of  his  lecture-room. 

75.  The  Pitch  of  the  Note  given  by  a  Sounding  Flame  de- 
pends upon  the  Length  of  the  Tube.  —  In  Figure  5 1  we  have 
a  glass  tube  held  over  a  gas-jet.  By  means  of  the  paper 
slider  s,  this  tube  may  be  lengthened  or  shortened.  While 
the  flame  is  sounding,  raise  the  slider  and  the  pitch  falls  ; 
lower  the  slider,  and  the  pitch  rises.  By  the  reaction  of 
the  pulses  reflected  upon  the  flame,  its  flutter  is  made 
periodic,  the  length  of  the  period  being  determined,  as  in 
the  case  of  organ-pipes,  by  the  length  of  the  tube. 


76.  In  a  Sounding  Flame  the  Gas  is  alternately  extin- 
guished and  relighted.  —  In  Figure  52,  A  B  is  a  glass  tube 
6  feet  long  and  2  inches  wide.  The  lower  part  of  the  tube 
is  blackened,  except  a  small  place  at  f.  M  is  a  concave 
mirror,  which  forms  upon  a  screen  an  enlarged  image  of 
the  flame.  By  turning  the  mirror,  the  image  may  be 
made  to  pass  over  the  screen.  On  twirling  the  mirror, 
we  obtain  a  series  of  images  o  p.  If  the  lower  end  be 
partially  closed  with  the  hand,  so  as  to  stop  the  vibration 
of  the  flame,  we  get  a  continuous  band  of  light  when  the 
mirror  is  twirled.  If  we  remove  the  hand  again,  this  band 
instantly  breaks  up  into  a  beaded  line  of  images. 


SOUND. 


77 


In  this  way  Professor  Tyndall  has  found  that  the  spaces 
between  the  images  of  a  singing  flame  are  absolutely  dark. 
If  so,  the  flame  must  be  extinguished  and  relighted  at  reg- 


Fig.  52- 


ular  intervals.  By  means  of  a  siren,  the  rate  at  which  a 
singing  flame  vibrates,  and  the  rapidity  with  which  it  is 
put  out  and  lighted  again,  may  be,  determined.  Professor 


78  SOUND. 

Tyndall  found  that  a  flame  with  which  he  was  experi- 
menting was  thus  put  out  and  relighted  453  times  in  a 
second. 

77.  The  Pitch  of  the  Note  produced  by  a  Sounding  Flame 
.depends  somewhat  on  the  Size  of  the  Flame.  —  A  singing 
flame  yields  so  freely  to  the  pulses  that  fall  upon  it,  that  it 
is  almost  wholly  governed  by  the  tube  which  surrounds  it ; 
but  the  pitch  of  the  note  depends  in  some  measure  upon 
the  size  of  the  flame.      This  can  be  proved  by  causing  two 
flames  to  give  out  the  same  note,  and  then  slightly  altering 
the  size  of  one  of  them.     The  discord  which  results  shows 
that  the  pitch  of  the  note  has  been  changed. 

If  we  take  a  long  tube  and  make  it  sound  its  funda- 
mental note,  we  can  obtain  the  octave  and  other  overtones 
of  that  note  by  altering  the  size  of  the  flame. 

78.  Sensitive  Flames  within   Tubes. — Place  a  tube   12 
inches  long  over  a  small  gas-flame,  so  that  the  flame  shall 
be  about  an  inch  and  a  half  from  the  bottom  of  the  tube. 
If  the  note  to  which  the  tube  would  resound  be  sounded  at 
some  distance,  the  flame  is  seen  to  tremble.     Lower  the 
tube,  so  that  the  flame  shall  be  about  three  inches  from  the 
bottom,  and  the  flame  begins  to  sing.     Now  it  is  possible 
to  find  somewhere  between  these  two  points  a  point  where 
the  flame  will  burn  silently ;  but  if  it  be  excited  by  the 
voice  it  will  sing,  and  keep  on  singing. 

In  this  position,  then,  it  is  able  to  sing,  but  it  needs  a 
start.  It  is,  as  it  were,  on  the  brink  of  a  precipice,  but  it 
requires  to  be  pushed  over.  By  placing  a  finger  for  an  in- 
stant on  the  end  of  the  tube,  we  can  stop  its  music.  If 
now  we  stand  as  far  away  from  it  as  the  room  will  allow, 
and  sound  the  proper  note/the  flame  at  once  begins  to 
sing  again.  It  makes  no  difference  whether  we  face 
the  flame  or  stand  with  the  back  towards  it,  —  whether  we 
sound  the  note  with  the  voice  or  with  any  musical  in' 
strument. 


SOUND.  79 

Let  there  be  two  small  flames,  a  and  b,  some  way  apart, 
with  a  tube  over  a  about  10  inches  long,  and  one  over  b 
about  12  inches  long.  A  paper  slider  is  fitted  to  the 
shorter  tube  so  that  its  length  may  be  varied.  Arrange  the 
tubes  so  that  the  flame  in  a  shall  sing  while  that  in  b  is 
silent.  If  now  we  raise  the  paper  slider  which  surrounds 
a  so  as  to  lengthen  the  tube,  when  the  pitch  of  this  tube 
comes  near  enough  to  that  of  the  other  the  flame  b  begins 
to  sing.  The  experiment  may  be  varied  by  making  b  the 
singing  flame,  and  a  the  silent  one  at  starting.  On  draw- 
ing up  the  slider  a  point  will  soon  be  reached  where  the 
flame  a  will  begin  to  sing. 

This  shows  that  a  singing  flame  may  cause  a  silent  one 
to  begin  to  sing. 

Flames  which  are  thus  affected  by  musical  sounds  are 
called  sensitive  flames. 

SUMMARY. 

Friction  is  always  rhythmic. 

When  a  gas-flame  is  surrounded  by  a  tube,  the  air  in 
passing  over  it  is  thrown  into  vibrations,  and  musical 
sounds  are  produced.  (74.) 

The  pitch  of  the  note  given  by  a  sounding  flame  de- 
pends mainly  on  the  length  of  the  tube  by  which  it  is 
surrounded,  but  somewhat  upon  the  size  of  the  flame. 

(75,  77-) 

A  silent  flame  within  a  tube  may  be  made  to  sing  by 
sounding  the  note  of  the  tube  near  it.  (78.) 

NOTE.    For  an  account  of  sensitive  naked  flames  see  Appendix,  II. 


80  SOUND. 


THE   HUMAN   VOICE. 

79.  The  Organ  of  Voice  a  Reed  Instrument.  — The  organ 
of  voice  in  man  is  situated  at  the  top  of  the  windpipe,  or 
trachea,  which  is  the  tube  through  which  the  air  is  blown 
from  the  lungs.  A  pair  of  elastic  bands,  called  the  vocal 
chords,  stretched  across  the  top  of  the  windpipe  so  as  nearly 
to  close  it,  form  a  double  reed.  When  the  air  is  forced  from 
the  lungs  through  the  slit  between  these  chords,  they  are 
made  to  vibrate.  By  changes  in  their  tension  their  rate  of 
vibration  is  varied,  and  the  sound  raised  or  lowered  in 
pitch.  The  cavity  of  the  mouth  and  nose  acts  as  a  res- 
onant tube. 

The  action  of  the  vocal  chords  may  be  imitated  by 
means  of  india-rubber  bands.  If  the  open  end  of  a  glass 
tube  be  closed  by  two  strips  of  india-rubber,  leaving  a 
slit  between  them,  and  the  air  be  blown  through  this  slit, 
the  strips  are  thrown  into  vibration,  and  a  musical  sound 

is  produced.  Helmholtz  rec- 
ommends the  form  shown  in 
Figure  53,  where  the  tube,  in- 
stead of  being  cut  off  square, 
ends  in  two  oblique  sections, 
over  which  the  rubber  bands 
are  stretched. 

The  easiest  way  of  making 
such  a  reed  is  to  wrap  round 
the  end  of  a  glass  tube  a  strip 

of  thin  india-rubber,  leaving  about  an  inch  of  the  substance 
projecting  beyond  the  end  of  the  tube.  Take  two  opposite 
portions  of  the  projecting  rubber  in  the  fingers,  and  stretch 
them,  so  as  to  form  a  slit.  On  blowing  through  this  slit  a 
musical  sound  is  produced  which  varies  in  pitch  as  the 
sides  of  the  slit  vary  in  tension. 


SOUND.  8 1 

80.  Vowel  Sounds.  —  We  can  readily  distinguish  one 
vowel  sound  from  another,  even  when  both  are  of  the 
same  pitch  and  intensity.  What  then  is  the  real  difference 
between  them  ? 

Fix  a  reed  in  a  frame  without  any  pipe  connected  with 
it.  Force  air  through  it  with  a  bellows,  and  it  speaks  for- 
cibly. Fix  now  upon  the  frame  a  pyramidal  pipe,  and  the 
clang-tint  changes  at  once.  Push  the  flat  hand  over  the 
open  end  of  the  pipe,  and  sounds  are  produced  very  much 
like  those  of  the  human  voice.  If  we  close  the  end  of  the 
pipe  entirely  with  the  palm  of  the  hand,  and  then  raise  the 
hand  twice  in  quick  succession,  the  word  "  mamma  "  is  dis- 
tinctly uttered.  If  the  same  experiment  be  repeated  with 
a  shorter  pyramidal  tube,  the  word  "  mamma  "  is  given  as 
it  would  be  uttered  by  a  child  with  a  stopped  nose.  Thus, 
by  connecting  a  suitable  pipe  with  a  vibrating  reed,  we  can 
give  to  the  sound  of  the  reed  the  qualities  of  the  human 
voice. 

Now,  in  the  vocal  organ  of  man  we  have  the  reed  in  the 
vocal  chords,  and,  connected  with  this,  the  resonant  cavity 
of  the  mouth,  which  can  so  alter  its  shape  as  to  resound 
either  to  the  fundamental  tone  of  the  vocal  chords,  or  to 
any  of  their  overtones.  By  means  of  the  mouth,  then,  we 
can  mix  together  the  fundamental  tone  and  the  overtones 
of  the  voice  in  different  proportions,  and  the  different  vowel 
sounds  are  the  result.  The  cavity  of  the  mouth  may  be 
made  to  resound  by  means  of  tuning-forks  ;  and  it  is  found 
that  when  it  is  adjusted  so  as  to  resound  to  a  certain  fork, 
only  one  particular  vowel  sound  can  be  produced  by  for- 
cing air  from  the  lungs  across  the  vocal  chords.  If  the 
cavity  is  adjusted  so  as  to  resound  to  a  fork  of  different 
pitch,  only  one  vowel  sound  can  be  produced,  but  it  is  dif- 
ferent from  the  one  obtained  before ;  and  so  on.  In  all 
these  cases,  if  the  vowels  are  uttered  with  the  same  pitch 
and  intensity,  the  condition  of  the  vocal  chords  is  not 
4*  F 


82  SOUND. 

changed.  They  give  throughout  the  same  fundamental 
tone  and  the  same  overtones  ;  and  the  different  vowel 
sounds  obtained  are  due  solely  to  the  fact  that,  in  the 
different  cases,  different  tones  have  been  reinforced  by  the 
resonance  of  the  mouth. 

Retaining  the  same  fundamental  tone,  by  adding  other 
tones,  or  by  varying  the  intensity  of  the  fundamental  tone 
or  of  one  or  more  of  the  overtones,  we  can  alter  the  qual- 
ity of  the  clang  (30),  and  thus  produce  the  different  clang- 
tints  ^f  the  human  voice. 

SUMMARY. 

The  vocal  organ  in  man  is  a  reed  instrument,  the  vibrat- 
ing reed  being  a  pair  of  elastic  bands  at  the  top  of  the 
windpipe,  which  are  capable  of  different  degrees  of  ten- 
sion. (30.) 

By  connecting  suitable  pipes  with  reeds,  we  can  give  to 
their  tones  the  qualities  of  the  human  voice. 

The  rate  of  vibration  of  the  vocal  chords  is  but  little 
affected  by  the  resonance  of  the  mouth  ;  but  the  mouth, 
by  changing  its  shape,  can  be  made  to  resound  to  the  fun- 
damental tone,  or  to  any  of  the  overtones  of  the  vocal 
chords.  By  strengthening  particular  tones  through  the 
resonance  of  the  mouth,  we  can  change  the  clang-tint  of 
the  voice. 

The  different  vowel  sounds  result  from  different  mix- 
tures of  the  fundamental  tone  and  the  overtones  of  the 
vocal  chords.  (80.) 


SOUND. 


THE   HUMAN   EAR. 


8 1.  A  section  of  the  human  ear  is  shown  in  Figure  54. 
In  this  organ  we  have,  first  of  all,  the  external  opening  of 
the  ear,  which  is  closed  at  the  bottom  by  a  circular  mem- 
brane called  the  tympanum.  Behind  this  is  the  cavity 


Fig.  54- 


called  the  drum  of  the  ear.  This  cavity  is  separated  from 
the  space  between  it  and  the  brain  by  a  bony  partition,  in 
which  there  are  two  openings,  the  one  round  and  the  other 
oval.  These  also  are  closed  by  delicate  membranes. 
Across  the  cavity  of  the  drum  stretches  a  series  of  four 
little  bones  :  the  first,  called  the  hammer,  is  attached  to  the 
tympanum  ;  the  second,  called  the  anvil,  is  connected  by  a 
joint  with  the  hammer ;  a  third  little  round  bone  connects 
the  anvil  with  the  stirrup  bone,  which  has  its  oval  base 
planted  against  the  membrane  of  the  oval  opening,  almost 
covering  it.  Behind  the  bony  partition,  and  between  it 
and  the  brain,  we  have  the  extraordinary  organ  called  the 
labyrinth,  which  is  filled  with  water,  and  over  the  lining  of 


84  SOUND. 

which  the  fibres  of  the  auditory  nerve  are  distributed. 
The  tympanum  intercepts  the  vibrations  of  the  air  in  the 
external  ear,  and  transmits  them  through  the  series  of 
bones  in  the  drum  to  the  membrane  which  separates  the 
drum  from  the  labyrinth  ;  and  thence  to  the  liquid  within 
the  labyrinth  itself,  which  in  turn  transmits  them  to  the 
nerves.  The  transmission  is  not,  however,  direct.  At  a 
certain  place  within  the  labyrinth,  exceedingly  fine  elastic 
bristles,  terminating  in  sharp  points,  grow  up  between  the 
nerve  fibres.  These  bristles,  discovered  by  Max  Schultze, 
are  exactly  fitted  to  sympathize  with  those  vibrations  of  the 
water  which  correspond  to  their  proper  periods.  Thrown 
thus  into  vibration,  the  bristles  stir  the  nerve  fibres  which 
lie  between  their  roots,  and  the  nerve  transmits  the  impres- 
sion to  the  brain  and  thus  to  the  mind.  At  another  place 
in  the  labyrinth  we  have  little  crystalline  particles  called 
otoliths, — the  Horsteinevi  the  Germans, — embedded  among 
the  nervous  filaments,  and  exerting,  when  they  vibrate, 
an  intermittent  pressure  upon  the  adjacent  nerve  fibres. 
The  otoliths  probably  answer  a  different  purpose  from  that 
of  the  bristles  of  Schultze.  '  They  are  fitted,  by  their 
weight,  to  receive  and  prolong  the  vibrations  of  evanes- 
cent sounds,  which  might  otherwise  escape  attention.  The 
bristles  of  Schultze,  on  the  contrary,  because  of  their  ex- 
treme lightness,  would  instantly  yield  up  an  evanescent 
motion,  while  they  are  peculiarly  fitted  for  the  transmission 
of  continuous  vibrations.  Finally,  there  is  in  the  labyrinth 
a  wonderful  organ,  discovered  by  Corti,  which  is  to  all 
appearance  a  musical  instrument,  with  its  chords  so 
stretched  as  to  receive  vibrations  of  different  periods 
and  transmit  them  to  the  nerve  filaments  which  traverse 
the  organ.  Within  the  ear  of  man,  and  without  his  knowl- 
edge or  contrivance,  this  lute  of  3,000  strings  *  has  existed 

*  According  to  Kolliker,  this  is  the  number  of  fibres  in  Corti's 
organ. 


SOUND.  85 

for  ages,  receiving  the  music  of  the  outer  world,  and  ren- 
dering it  fit  for  reception  by  the  brain.  Each  musical 
tremor  which  falls  upon  this  organ  selects  from  its  tense 
fibres  the  one  appropriate  to  its  own  pitch,  and  throws  that 
fibre  into  sympathetic  vibration.  And  thus,  no  matter  how 
complicated  the  motion  of  the  external  air  may  be,  these 
microscopic  strings  can  analyze  it,  and  reveal  the  elements 
of  which  it  is  composed. 

Such  are  the  views  now  entertained  by  the  most  eminent 
authorities  as  to  the  transmission  of  sonorous  motion  to 
the  auditory  nerve.  They  are  not  to  be  considered  as  es- 
tablished, but  only  as  probable. 

82.  The  Range  of  the  Human  Ear.  —  We  have  already 
seen  that  vibrations  cease  to  blend  into  one  sound  when 
they  are  very  slow.  Helmholtz  has  found  that  there  must 
be  at  least  16  vibrations  in  a  second  in  order  that  they  may 
be  heard  as  a  continuous  sound.  Depretz  has  shown  that 
the  sound  ceases  to  be  audible  when  the  vibrations  reach 
38,000  in  a  second.  Starting  with  16  and  multiplying 
continually  by  2,  we  find  that  the  nth  octave  will  have 
32,768  vibrations.  The  entire  range  of  the  human  ear, 
then,  extends  to  about  n  octaves.  The  practical  range 
of  musical  sounds  is  from  40  to  4,000  vibrations  in  a  sec- 
ond, or  about  7  octaves. 

The  limits  of  hearing  are  different  in  different  persons. 
Dr.  Wollaston,  to  whom  we  owe  the  first  proof  of  this, 
found  that  one  of  his  friends  could  not  hear  the  sound  of  a 
small  organ-pipe,  the  sharpness  of  which  was  far  within  the 
ordinary  limits  of  hearing.  The  squeak  of  the  bat,  the 
sound  of  a  cricket,  even  the  chirrup  of  the  English  house- 
sparrow,  are  unheard  by  some  people  who  possess  a  sensi- 
tive ear  for  lower  sounds.  The  ascent  of  a  single  note  is 
sometimes  sufficient  to  produce  the  change  from  sound  to 
silence.  "  The  suddenness  of  the  transition,"  writes  Wol- 
laston, "  from  perfect  hearing  to  total  want  of  perception; 


86  SOUND. 

occasions  a  degree  of  surprise  which  renders  an  experi- 
ment of  this  kind  with  a  series  of  small  pipes  among  sev- 
eral persons  rather  amusing.  It  is  curious  to  observe  the 
change  of  feeling  manifested  by  various  individuals  of  the 
party,  in  succession,  as  the  sounds  approach  and  pass  the 
limits  of  their  hearing.  Those  who  enjoy  a  temporary 
triumph  are  often  compelled,  in  their  turn,  to  acknowledge 
to  how  short  a  distance  their  little  superiority  extends." 
"  Nothing  can  be  more  surprising,"  writes  Sir  John  Her- 
schel,  in  reference  to  this  subject,  "  than  to  see  two  per- 
sons, neither  of  them  deaf,  the  one  complaining  of  the 
penetrating  shrillness  of  a  sound,  while  the  other  maintains 
there  is  no  sound  at  all.  Thus,  while  one  person  men- 
tioned by  Dr.  Wollaston  could  but  just  hear  a  note  4  octaves 
above  the  middle  E  of  the  pianoforte,  others  have  a  dis- 
tinct perception  of  sounds  full  2  octaves  higher.  The  chir- 
rup of  the  sparrow  is  about  the  former  limit ;  the  cry  of  the 
bat  about  an  octave  above  it ;  and  that  of  some  insects 
probably  another  octave."  In  "  The  Glaciers  of  the  Alps  " 
Professor  Tyndall  relates  that  while  crossing  the  Wengern 
Alp  he  found  that  a  friend  who  was  with  him  could  not 
hear  the  shrill  music  of  the  swarms  of  insects  in  the  grass 
on  the  sides  of  the  path,  though  to  himself  the  sound 
seemed  to  rend  the  air. 

It  may  be  remarked  that  the  shrill  notes  of  many  insects 
are  the  result  of  the  rapid  vibrations  of  their  wings, 
amounting  sometimes  to  more  than  16,000  in  a  second. 

SUMMARY. 

The  human  ear  consists  of  three  parts :  the  outer  ear, 
the  drum,  and  the  labyrinth. 

The  sonorous  vibrations  are  first  intercepted  by  the  tym- 
panum, then  transmitted  to  the  fluid  in  the  labyrinth,  and 
then  again  intercepted  by  the  bristles  of  Schultze,  the  oto- 


SOUND.  87 

liths,  and  the  fibres  of  Corti,  by  which  they  are  communi- 
cated to  the  auditory  nerve.     (81.) 

The  range  of  human  hearing  embraces  about  eleven 
octaves.  (82.) 

CONCLUSION. 

Sound  originates  in  a  vibrating  body,  and  is  transmitted 
through  air  and  other  elastic  media  by  means  of  waves, 
with  a  velocity  which  increases  with  the  ratio  of  the  elastici- 
ty to  the  density.  Its  velocity  in  air  at  the  freezing-point 
is  1,090  feet  a  second.  When  sound-waves  meet  a  medium 
different  from  that  in  which  they  are  moving,  they  are  par- 
tially reflected  and  partially  transmitted.  In  the  reflected 
portion  the  angle  of  reflection  is  always  equal  to  the  angle 
of  incidence.  The  transmitted  portion  is  refracted,  either 
away  from  or  towards  a  perpendicular  to  the  surface  of  the 
new  medium,  according  as  the  velocity  of  sound  is  greater 
or  less  in  this  medium  than  in  the  old. 

Bodies  which  vibrate  regularly  and  with  sufficient  rapid- 
ity produce  musical  sounds.  The  pitch  of  the  sound  in- 
creases with  the  rapidity  of  the  vibrations ;  and  the  inten- 
sity, with  the  amplitude  of  the  vibrations.  All  sounding 
bodies  are  capable  of  originating  vibrations  of  several 
different  periods  at  the  same  time,  and  the  blending  of 
these  vibrations  produces  the  quality  or  clang-tint  of  the 
sound.  Sonorous  bodies  are  capable  of  taking  up  from  the 
air  and  other  elastic  media  those  vibrations  which  are 
synchronous  with  their  own,  and  in  this  way  they  are 
thrown  into  sympathetic  vibrations. 

In  passing  through  the  air  different  sound-waves  may 
coincide  so  as  to  increase  their  volume,  or  else  interfere  so 
as  partially  or  wholly  to  destroy  one  another.  When  meet- 
ing in  alternating  phases,  sound-waves  give  rise  to  beats,  and, 
if  of  sufficient  volume,  to  resultant  tones.  Dissonance  is 
caused  by  a  /apid  succession  of  beats. 


88  SOUND. 

The  rapidity  of  the  transverse  vibrations  of  strings  de- 
pends upon  their  length,  their  tension,  and  their  weight. 
By  varying  these  we  can  produce  a  regular  succession  of 
musical  sounds,  as  in  stringed  instruments. 

The  rapidity  of  the  longitudinal  vibrations  of  rods  varies 
with  their  length  and  elasticity.  By  means  of  such  vibrat- 
ing rods  we  can  measure  the  velocity  of  sound  in  different 
solids.  A  column  of  air  can  be  thrown  into  longitudinal 
vibrations  by  a  tuning-fork,  by  a  fluttering  current  at  the 
mouth  of  the  tube  which  contains  the  column,  and  by  a  reed. 
The  rapidity  of  the  vibrations  depends  upon  the  length  of 
the  column.  By  causing  columns  of  gases  and  liquids  to 
vibrate,  we  can  measure  the  velocity  of  sound  in  each. 
In  wind  instruments  musical  sounds  are  produced  by  means 
of  vibrating  columns  of  air.  In  singing  flames  the  column 
of  air  is  made  to  vibrate  by  the  fluttering  of  the  flame. 

The  human  organ  of  voice  is  a  reed  instrument,  and  the 
different  vowel  sounds  are  produced  by  altering  the  reso- 
nant cavity  of  the  mouth  and  nose,  so  as  to  cause  it  to 
reinforce  different  overtones  of  the  vocal  chords. 

The  human  ear  is  an  apparatus  for  intercepting  the  vi- 
brations of  the  external  air  and  transmitting  them  to  the 
auditory  nerve. 


II. 

LIGHT. 


NATURE   AND    PROPAGATION   OF 
LIGHT. 


RADIATION. 

83.  A  body  in  which  light  is  developed  is  called  a  lumi- 
nous body.     All  other  bodies  are  said  to  be  non-luminous. 

84.  A  Luminous  Body  sends  out  Light  in  Every  Direction. 
—  It  is  well  known  that,  if  a  lighted  lamp  is  placed  in  the 
middle  of  a  room,  it  illumines  every  part  of  the  room  ; 
showing  that  the  light  proceeds  from  the  luminous  body  in 
every  direction. 

A  body  through  which  light  passes,  as  air  and  glass, 
is  said  to  be  transparent.  Other  bodies  are  said  to  be 
opaque. 

85.  Light  travels  through  Space  in  Straight  Lines.  —  If  a 
room  be  darkened,  and  the  sunlight  be  allowed  to  enter 
through  a  small  hole  in  the  shutter,  it  will  illumine  the 
floating  particles  of  dust  in  the  air  through  which  it  passes, 
so  that  we  can  trace  its  path  ;  and  in  every  case  we  find 
that  it  moves  in  a  straight  line.     It  is  for  this  reason  that 
we  cannot  see  an  object  when  there  is  any  opaque  body 
between  it  and  the  eye. 

When  an  opaque  body  is  placed  before  a  luminous  one, 
it  cuts  off  the  light  from  the  space  behind  it,  producing 
wha.t  is  called  a  shadow. 

If  the  luminous  body  S  (Figure  55)  is  a  mere  point, 
the  body  J/will  cast  a  well-defined  shadow  (9Zf  upon  the 


92 

screen  P  Q.     If  the  straight  line  S  G  be  carried  round  the 
sphere  M,  touching  it  all  the  time,  the  part  M  G  will  ex- 
Fig.  55- 


actly  mark  the  limits  of  the  shadow  cast  by  M.  The  form 
of  this  shadow,  then,  shows  that  light  moves  through  the 
air  in  straight  lines. 

If  the   luminous  body  is  not  a  mere  point,   then  the 
shadow  cast  by  the  sphere  M N (Figure  56)  will  have  an 

Fig.  56. 


indistinct  outline.  The  reason  of  this  is  evident.  If  the 
line  S  G  be  carried  round,  touching  both  spheres  all  the 
time,  the  portion  M  G  will  mark  out  the  space  within  which 
no  ray  of  light  from  S  L  can  enter.  Around  this  space 
there  will  be  a  space  from  which  a  part  of  the  light  of  SL 
is  cut  off.  This  extends  to  the  outer  circle  D  C ;  for  it  is 
evident  that  light  from  S  can  pass  into  the  space  between 
D  and  <9,  while  it  is  cut  off  from  the  space  between  C  and 
H;  and  light  from  L  can  pass  into  the  space  between  Cand 
H,  while  it  is  cut  off  from  that  between  D  and  G.  As  we 
proceed  from  the  outer  ring  D  C  to  the  inner  one  G  H^ 
more  and  more  of  the  light  from  S  L  is  cut  off,  so  that  the 


LIGHT.  93 

shadow,  instead  of  being  sharply  defv*^d,  fades  gradually 
into  the  light.  The  dark  central  portion  G  H  of  the  shadow 
is  called  the  umbra ;  the  less  dark  outer  portion  is  called 
the  penumbra.  Umbra  is  the  Latin  word  for  shadow1-  while 
penumbra  means  almost  a  shadow. 

86.  Rays.  —  Since  a  luminous  body  gives  out  light  in 
every  direction  in  straight  lines,  it  is  said  to  radiate  light. 
A  single  line  of  light  is  called  a  ray.     A  collection  of  rays 
is  called  a  pencil.     If  the  rays  are  parallel,  it  is  a  parallel 
pencil,  or  a  beam  ;  if  the  rays  diverge,  it  is  a  divergent  pen 
cil ;  if  they  converge,  a  convergent  pencil. 

87.  The  Velocity  of  Light.  —  Light  moves  so  fast  that  it 
seems  to  require  no  time  at  all  to  pass  over  any  distance  on 
the  earth.     Its  velocity  was  first  determined  by  Romer,  a 
Danish  astronomer,  in  1675,  by  observing  the  eclipses  of 
Jupiter's  moons.      Jupiter,  like  the  earth,  is  a  planet  which 
revolves  about  the  sun,  but  at  a  much  greater  distance  than 

FIT.  *T. 


the  earth.  He  is  accompanied  by  four  moons,  which  are 
eclipsed  when  they  pass  into  his  shadow.  In  Figure  57, 
let  5  represent  the  sun,  T'the  earth,  and/ Jupiter.  Romei 
found  on  watching  the  eclipses  of  one  of  the  moons,  that 
while  the  earth  was  moving  from  T  to  7",  the  intervals  be- 
tween the  eclipses  grew  longer  and  longer,  and  that  while 


94  LIGHT. 

the  earth  was  passing  from  T'  round  to  T  again,  they  be- 
came shorter  and  shorter;  while  they  should  have  remained 
constantly  the  same.  Now  it  is  evident  that  we  should  not 
be  aware  of  the  eclipse  until  the  light  which  left  the  moon 
just  as  it  entered  the  shadow  had  reached  us ;  and  that  as 
the  earth  passes  from  Tto  T'  the  distance  which  this  light 
must  travel  is  continually  increasing,  while  as  the  earth 
passes  from  T'  to  T  this  distance  is  continually  decreas- 
ing. If,  then,  light  requires  time  to  pass  over  this  distance, 
the  interval  between  the  eclipses  should  lengthen  in  the 
one  case  and  shorten  in  the  other.  Romer  found  that 
the  increase  in  the  intervals  while  the  earth  was  passing 
from  T  to  T'  amounted  to  16  minutes;  that  is,  the  eclipses 
at  T'  occurred  16  minutes  later  than  they  would  have 
occurred  had  the  earth  remained  at  T.  He  therefore  con- 
cluded that  it  takes  light  about  16  minutes  to  cross  the 
earth's  orbit,  a  distance  of  about  190,000,000  miles.  Its 
velocity  then  would  be  about  192,000  miles  a  second. 

88.  The  Intensity  of  Light  diminishes  as  the  Square  of  1he 
Distance  from  the  Luminous  Body  increases.  —  In  Figure  58 
the  disc  C  D  is  held  half-way  between  the  luminous  point 

Fig.  58. 


L  and  the  screen  A  B.  If  the  disc  is  held  parallel  to 
the  screen,  the  diameter  of  the  shadow  on  the  screen  will 
be  twice  that  of  the  disc,  and  its  surface  will  be  four  times 
that  of  the  disc.  The  disc  receives  all  the  light  that  the 
space  covered  by  the  shadow  would  receive  if  the  disc 
were  removed.  The  light  on  the  disc  must  then  be  four 


LIGHT. 


95 


times  as  intense  as  that  upon  the  screen.  If  the  disc  is 
held  one  third  of  the  way  between  L  and  the  screen,  the 
shadow  will  cover  a  surface  nine  times  that  of  the  disc, 
and  the  intensity  of  the  light  on  the  disc  will  be  nine  times 
as  great  as  that  upon  the  screen  •  and  so  on.  The  inten- 
sity of  the  light,  then,  diminishes  as  the  square  of  the  dis- 
tance increases. 

89.  Photometers.  —  An  instrument  for  measuring  the 
relative  intensity  of  lights  is  called  a  photometer.  One 
of  the  simplest  is  that  of  Count  Rumford,  shown  in  Fig- 
ure 59.  An  opaque  rod  m  is  placed  in  front  of  a  ground- 


Fig.  59- 


glass  screen.  The  lights  to  be  compared,  as  L  and  B,  are 
placed  in  such  a  way  that  each  casts  the  shadow  of  the  rod 
upon  the  screen.  Their  distances  are  then  made  such  that 
the  two  shadows  a  and  b  are  of  exactly  the  same  intensity. 
The  screen  must,  then,  be  receiving  the  same  amount  of 
light  from  L  and  B  ;  for  the  shadow  cast  by  B  is  illumined 
by  Z,  and  that  cast  by  L  is  illumined  by  B.  To  find  now 
the  intensity  of  the  light  from  the  two  sources,  measure  the 
distance  of  each  from  the  screen.  These  distances  are  to 
each  other  as  the  square  roots  of  the  intensities  of  the  lights ; 
and  the  intensities  of  the  lights  are  to  each  other  as  the 
squares  of  the  distances. 


96  LIGHT. 


SUMMARY. 

A  luminous  body  gives  out  light  in  every  direction,  which 
passes  through  space  in  straight  lines.  (84,  85.) 

A  single  line  of  light  is  called  a  ray,  and  a  collection  of 
rays,  a  beam,  or  pencil.  (86.) 

Light  traverses  space  with  a  velocity  of  about  190,000 
miles  a  second.  (87.) 

The  intensity  of  light  diminishes  as  the  square  of  the 
distance  increases.  (88.) 

The  intensity  of  light  is  measured  by  means  of  the 
photometer.  (89.) 

REFLECTION   AND   REFRACTION. 

r  i  -X, 

90.  If  a  ray  of  sunlight  be  let  into  a  darkened  room,  and 
allowed  to  fall  upon  a  looking-glass,  it  will  be  seen  to  be 
thrown  back  from  the  glass.  Light  thus  thrown  back  is 
said  to  be  reflected. 

A  piece  of  glass  cut  into  the  form  shown  in  Figure  60  is 
called  a  prism. 

Fig.  60.  Fig.  61. 


If  a  ray  of  light,  a  b,  be  allowed  to  fall  obliquely  upon 
one  side  of  such  a  prism,  as  shown  in  Figure  61,  a  part  of 
the  light  is  seen  to  be  reflected  in  the  direction  b  <r,  and  an- 
other part,  b  d,  to  enter  the  prism.  It  will  be  seen  that  the 
part  which  enters  the  prism  is  bent  from  the  direction  of 


LIGHT.  97 

the  original  ray.  When  this  part  meets  the  air  at  the  op- 
posite side  of  the  prism,  a  part  of  it  is  again  reflected 
in  the  direction  d  e,  and  a  part  passes  into  the  air,  taking 
a  different  direction,  df,  from  that  which  it  had  while  in 
the  prism. 

We  see,  then,  that  when  light  travelling  in  the  air  meets 
the  glass,  it  is  partly  reflected  and  partly  transmitted  ;  and 
that  when  light  travelling  in  the  glass  meets  the  air  again, 
it  is  also  partly  reflected  and  partly  transmitted.  In  both 
cases  the  transmitted  portion  is  turned  aside  from  its 
course.  Light  thus  turned  aside  is  said  to  be  refracted. 

It  is  found  that,  in  general,  when  light  meets  a  transpar- 
ent medium  different  from  that  which  it  has  been  travers- 
ing, it  is  partly  reflected  and  partly  refracted. 

If  a  ray  of  light  be  allowed  to  fall  upon  a  piece  of 
polished  steel,  it  will  be  seen  that  light  is  also  reflected  on 
meeting  with  an  opaque  body. 

91.  The  Law  of  Reflection.  —  In  Figure  62,  we  have  a 

Fig.  62. 


plane  mirror  Z  fastened  at  right  angles  to  the  rod  m  n,  and 
turning  upon  a  pivot  at  n.  As  the  mirror  is  turned  to  the 
right  or  left,  the  rod  passes  over  the  graduated  arc  a  b.  If 
a  ray  of  light  be  allowed  to  fall  upon  the  mirror  in  the  direc- 
tion of  the  dotted  line  a  n,  it  will  be  reflected  in  the  direc- 
tion of  the  line  n  b;  and  it  will  be  seen  that  the  angle  a  n  m 
5  G 


98  LIGHT. 

is  equal  to  the  angle  b  n  m.  The  former  is  called  the  angle 
of  incidence,  and  the  latter  the  angle  of  reflection.  Both  the 
incident  and  reflected  rays  lie  in  the  same  plane  with  the 
perpendicular.  If  the  mirror  be  turned,  the  direction  of 
the  reflected  ray  changes  in  such  a  way  that  the  angle  of  in- 
cidence always  equals  the  angle  of  reflection.  This  is  always 
true  of  reflected  light,  and  is  known  as  the  law  of  re- 
flection. 

92.  The  Intensity  of  Reflected  Light.  —  It  is  by  light  thus 
reflected  that  we  see  an  object  in  a  mirror  or  other  smooth 
surface.  If  we  hold  a  sheet  of  writing-paper  horizontally 
and  close  to  the  flame  of  a  lamp  or  candle  (Figure  63),  and 
Fig.  63.  put  the  eye  close  down  to 

the  paper,  as  at  a,  so  as  to 
receive  the  light  which  is 
reflected  very  obliquely,  a 
distinct  image  of  the  flame 
will  be  seen  on  the  paper. 
If  the  eye  be  placed  higher 
up,  as  at  b,  so  as  to  receive  the  light  reflected  less  obliquely, 
no  image  can  be  seen.  This  experiment  shows  that  the 
amount  of  light  reflected  depends  upon  the  angle  of  inci- 
dence, increasing  as  this  angle  increases. 

It  also  depends  upon  the  smoothness  of  the  surface. 
This  may  be  readily  seen  by  substituting  for  the  sheet  of 
paper  a  piece  of  looking-glass  or  polished  metal.  In 
this  case  the  image  of  the  candle  can  be  seen  at  any 
angle. 

The  reflection  is  found  to  vary  somewhat  with  different 
substances,  even  when  the  degree  of  polish  and  the  angle 
of  incidence  are  the  same. 

It  is  well  known  that  non-luminous  bodies  are  not  visible 
in  the  dark,  but  become  visible  when  light  falls  upon  them. 
It  is  evident,  then,  that  they  must  send  to  our  eyes  some 
of  the  light  they  receive.  This  light  must  be  sent  out  in 


LIGHT. 


99 


Fig.  64. 


every  direction,  since  we  can  see  them  as  well  from  one 
position  as  another.  The  light  which  they  thus  throw  off 
is  said  to  be  diffused.  It  is  this  diffused  light  which  en- 
ables us  to  see  the  body  itself;  while  reflected  light  en- 
ables us  to  see  another  body  in  it.  The  most  perfectly 
polished  mirror  does  not  reflect  all  the  light  it  receives.  It 
diffuses  a  portion,  so  that  we  see  the  mirror  as  well  as  the 
objects  reflected  in  it. 

93.  The  Law  of  Refraction.  —  The  bending  of  a  ray  of 
light  in  passing  from  one  medium  to  another  can  be  illus- 
trated by  the  apparatus  shown  in  Figure  64.  A  D  is  a 
graduated  circle ;  B,  a 
semi  -  cylindrical  glass  s/ 

vessel   filled   with  water  ** 

just  up  to  the  centre  of 
the  circle.  O  M  and 
O  P  are  two  arms,  each 
of  which  turns  about  the 
centre  of  the  circle.  One 
carries  a  mirror  M,  so 
arranged  as  to  throw  the 
ray  of  light  S  through  the 
opening  of  the  screen  N 
upon  the  surface  of  the 
water  exactly  at  the  cen- 
tre of  the  circle.  The 
other  arm  carries  a  small 
screen  P. 

In  order  that  the  refracted  ray  may  fall  upon  this  screen, 
we  find  that  the  arm  O  P  must  be  placed  so  as  to  make 
the  angle  D  O  P,  or  the  angle  of  refraction,  less  than  the 
angle  A  O  M,  or  the  angle  of  incidence,  showing  that  when 
a  ray  of  light  passes  from  air  into  water  it  is  bent  to- 
wards a  perpendicular  drawn  to  the  surface  of  the  water. 
This  is  found  to  be  always  true  when  the  light  passes  from 


100  LIGHT. 

a  rarer  to  a  denser  medium.  When  it  passes  from  a  denser 
to  a  rarer  medium,  it  is  bent  away  from  a  perpendicular 
drawn  to  the  surface  of  the  latter  medium.  For  instance,  if 
the  mirror  J/be  carried  round  to  P,  so  that  the  light  passes 
from  P  to  O,  it  will  be  found  that  on  passing  into  the  air 
again  it  takes  the  direction  O  M.  It  is  evident,  then,  that 
on  passing  from  water  into  air  it  is  bent  away  from  the  per- 
pendicular just  as  much  as  it  is  bent  towards  it  on  passing 
into  water. 

Suppose  the  mirror  M  to  be  moved  either  towards  or 

away  from  A;  the  screen  P  will  have  to  be  moved,  in  order 

to  receive  the  refracted  ray.     In  this  way  we  find  that  the 

angle  of  refraction  increases  with  the  angle  of  incidence. 

In  Figure  65  let  B  A  be  the  surface  of  a  denser  medium; 

P  Q,  a  perpendicular  to 
that  surface;  D  C P,  the 
angle  of  incidence  of  the 
ray  D  C;  E  C  Q  its  an- 
gle of  refraction  ;  and  M 
Na.  circle  described  about 
Cas  a  centre.  On  chang- 
ing the  angle  of  incidence, 
it  is  found  that  the  angle 
of  refraction  changes  in 
such  a  way  that  the  lines 
MR  and  N  S,  drawn  per- 
pendicular to  P  Q,  always 
have  the  same  ratio ;  that  is,  if,  for  any  value  of  the  angle 
of  incidence,  MR  is  twice  as  long  as  N S>  it  will  be  twice 
as  long  for  every  value.  These  lines  are  called  the  sines 
of  the  angles  D  CP&nd  JV  C  S,  and  the  law  of  refraction 
may  be  thus  stated  :  When  light  passes  from  one  medium  into 
another,  the  ratio  which  the  sine  of  the  angle  of  incidence  bears 
to  the  sine  of  the  angle  of  refraction  is  always  the  same  for 
the  same  media. 


LIGHT.  10 1 

It  is  found,  however,  that  this  ratio  varies  with  different 
media. 

Of  course,  when  the  incident  ray  is  perpendicular  to  the 
surface  of  the  new  medium,  no  refraction  takes  place. 

94.  Index  of  Refraction.  —  The  ratio  between  the  sines 
of  the  angles  of  incidence  and  refraction  is  called  the  index 
of  refraction.     This  index  varies  with  the  media.     For  ex- 
ample, from  air  to  water  it  is  f  ;  from  air  to  glass  £ ;  and 
so  on.     Of  course,  from  water  to  air,  it  will  be  £ ;  from 
glass  to  air  f ;  and  so  on. 

95.  Total  Reflection. — When  a  ray  of  light  passes  from 
a  denser  to  a  rarer  medium,  as  from  water  into  air,  the  angle 
of  refraction  is,  as  we  have  seen,  greater  than  the  angle  of 
incidence.     Hence  when  light  passes  through  water  from 
S  to  O  (Figure  66)  there  is  always  a  value  of  the  angle  of 

incidence  S  O  B  such  that  the  an-  ,,. 

£• 
gle  of  refraction  A  O  R  is  a  right 

angle.  In  this  case  the  ray  cannot 
pass  from  the  water  into  the  air.  If 
the  incident  angle  be  made  any 
larger,  the  light  is  thrown  back  in 
the  direction  of  Q.  In  this  case  it 
is  said  to  be  totally  reflected. 

This  total  reflection  may  be  illus- 
trated by  means  of  a  prism  whose  section  is  an  isosceles 
right  angled  triangle.      It  will  be 

Fig.  67. 

seen  that  none  of  the  light  (Figure 
67)  can  get  through  the  prism,  but 
it  is  all  reflected  in  the  direction 
HO. 

The  angle  at  which  light  in  pass- 
ing from  water  to  air  begins  to  be 
totally  reflected   is  48°  35';   from 
glass  to  air,  41°  48'.* 

*  See  Appendix,  III. 


102 


LIGHT. 


96.  Mirage.  —  In  hot  climates,  especially  on  the  sandy 
plains  of  Sahara  in  Africa,  the  ground  has  often  the  ap- 
pearance of  a  tranquil  lake,  on  which  are  seen  reflected 
houses  and  trees.  This  is  caused  by  total  reflection.  The 
layers  of  air  near  the  ground  are  more  heated,  and  there- 
fore less  dense  than  those  higher  up.  A  ray  of  light,  then, 
coming  from  A  (Figure  68)  is  bent  round  more  and  more 

Fig.  68. 


as  it  passes  down  through  the  successive  layers  until  it 
reaches  the  point  O,  where  the  angle  of  incidence  becomes 
such  that  it  is  totally  reflected,  and  reaches  the  eye  as  if  it 
came  from  A'.  The  same  will  be  true  of  light  coming 
from  other  parts  of  the  tree,  so  that  the  tree  will  appear 
inverted,  as  if  reflected  in  water.  This  phenomenon  is 
called  mirage,  and  often  deludes  the  thirsty  traveller  on  the 
desert  with  the  appearance  of  water  which  vanishes  as  he 
draws  near  it. 

Another  form  of  mirage,  the  reverse  of  this,  is  often  seen 
on  the  water.  In  this  case  the  layers  of  air  near  the  water 
are  colder  and  more  dense  than  those  above,  so  that  the 
rays  of  light  passing  upward  from  an  object  are  bent  round 
more  and  more,  until  at  last  they  are  totally  reflected  down- 


LIGHT.  103 

ward  to  the  eye  of  the  observer,  who  thus  sees  the  object 

inverted  in  the  air. 

97.  Some  of  the  Effects  of  Refraction.  —  Suppose  a  body 

to  be  at  L  (Figure  69)  beneath  the  surface  of  water.     The 

rays  of  light  coming  from  it  on  reaching  p.g 

the  surface  are  refracted  in  the  directions 

A  C  and  B  D,  so  that  they  appear  to  come 

from  the  point  L'.     Now  as  we  see  an  ob- 
ject in  the  direction  in  which  the  light  from 

it  reaches  the  eye,  the  object  L  will  appear 

to  be  at  Z',  or  higher  up  than  it  really  is. 

This  explains  why  it  is  that  a  stick  placed 

obliquely  in  the  water  appears  bent,  as  in  Figure  70.    Each 
Fig  70  part  of  the  stick  in  the  water  appears  to 

be  lifted  up  a  little  by  refraction. 

In  the  same  way  light  is  refracted  in 
passing  through  the  air,  and  since  the  air 
is  more  and  more  dense  as  it  is  nearer  the 
earth,  a  ray  of  light  is  bent  more  and  more 
as  it  approaches  the  earth.  Hence  we 
see  the  sun  and  the  stars  before  they  rise 

and  after  they  set.     It  will  be  evident  from  Figure  71  why 

it  is  that  we  always  see  a  heav-  FJ 

enly  body  higher  up  than  it 

really  is. 

Refraction   varies   with   the 

condition  of  the  atmosphere. 

Sometimes  at  sea  it  is  so  great 

that  objects  below  the  horizon, 

as  ships  and  islands,  are  lifted 

up  enough  to  become  visible. 

Occasionally  we  have  this  extraordinary  effect  of  refraction 

combined  with  mirage,  so  that  a  ship  which  is  really  below 

the  horizon  may  be  seen  suspended  in  the  air  with  its  in- 
verted image  beneath  it. 


104 


LIGHT. 


Fig.  12. 


98.  Path  of  Rays  through  a  Medium  with  Parallel  Faces. 
—  When  light  passes  through  a  medium  with  parallel  faces, 
the  rays  leave  this  medium  at  the  same  angle  at  which  they 
entered  it.     In  Figure  72  let  J/7V^be  a  plate  of  glass  with 

parallel  faces.  /  is  the  angle 
of  incidence  of  the  ray  S  A, 
and  r  the  angle  of  refraction  : 
?  is  the  angle  of  incidence  of 
the  same  ray  when  it  meets 
the  air  again,  and  /  the  angle 
of  refraction.  Since  the  ray 
in  passing  into  the  air  is  bent 
away  from  the  perpendicular 
just  as  much  as  it  was  bent  towards  it  in  passing  into  the 
glass,  the  angle  r1  will  evidently  be  equal  to  the  angle  i; 
that  is,  the  ray  leaves  the  glass  at  the  same  angle  at  which 
it  entered  it.  Its  direction,  therefore,  after  leaving  it  is 
the  same  as  before  entering  it. 

99.  Path  of  Rays  through  a  Prism.  —  In  Figure  73  let 
A  B  C  be   the  section  of  a  Fig.  73. 

prism.     The  ray  of  light  O  D 

on  passing  into  the  prism  is 

bent  towards  a  perpendicular 

drawn   to   the  surface  at  D. 

On  passing  out  into  the  air 

again  it  is  bent  away  from  a 

perpendicular    drawn    to    the 

surface  at  K.     We  see,  then,  that  a  ray  of  light  in  passing 

through  a  prism  is  bent  twice  in  the  same  direction,  unless 

it  meets  one  of  the  faces  perpendicularly. 


LIGHT.  105 


SUMMARY. 

When  light  falls  on  a  transparent  medium  different  from 
ihat  in  which  it  is  moving,  it  is  partially  reflected  and  par- 
tially refracted.  (90.) 

The  angle  of  reflection  equals  the  angle  of  incidence. 

(91.) 

The  amount  of  light  reflected  depends  upon  the  angle  of 
incidence,  the  polish  of  the  surface,  and  the  nature  of  the 
medium. 

All  bodies  diffuse  light,  and  it  is  by  means  of  this  diffused 
light  that  we  see  them. 

Light  is  also  reflected  from  opaque  surfaces.     (92.) 

The  ratio  of  the  sine  of  the  angle  of  incidence  to  that  of 
the  angle  of  refraction  always  remains  the  same  for  the 
same  medium,  but  is  different  for  different  media.  This 
ratio  is  called  the  index  of  refraction.  (93,  94.) 

On  meeting  a  rarer  medium  at  a  certain  angle,  light  is 
totally  reflected.  (95.) 

Mirage  and  other  atmospheric  phenomena  of  the  kind 
are  caused  by  irregular  refraction.  (96.) 

On  passing  through  a  medium  with  parallel  sides,  a  ray 
of  light  emerges  parallel  to  its  original  direction.  (98.) 

On  passing  through  a  prism,  a  ray  is  bent  twice  in  the 
same  direction.  (99.) 

DISPERSION. 

TOO.  The  Solar  Spectrum.  —  Allow  a  beam  of  sunlight, 
S  A  (Figure  74)  to  pass  through  a  small  opening  into  a 
darkened  room,  and  fall  upon  the  prism  P.  If  the  prism 
be  placed  at  the  proper  angle,  the  beam  of  light  is  not  only 
bent  from  its  course,  but  is  spread  out  so  as  to  form  a  long 
band  of  light  on  the  opposite  wall.  This  band  is  not  white, 
5* 


106  LIGHT. 

like  ordinary  sunlight,  but  made  up  of  the  seven  colors  of 
the  rainbow,  violet,  indigo,  blue,  green,  yellow,  orange,  and 
red.  This  colored  band  is  called  the  solar  spectrum. 

Fig.  74- 


When  prisms  of  different  substances  are  used,  the  spectra 
obtained  have  the  same  colors  and  in  the  same  order,  but 
are  of  different  lengths. 

This  spreading  out  of  a  beam  of  light  is  called  dispersion; 
and  the  power  of  any  substance  to  produce  this  effect  is 
called  its  dispersive  power.  We  might  think  that  the  dis- 
persive power  of  a  substance  would  be  in  proportion  to  its 
refractive  power,  but  this  is  not  the  case.  Thus  the  refrac- 
tive power  of  flint  glass  is  almost  the  same  as  that  of  crown 
glass,  but  its  dispersive  power  is  nearly  double.  The 
liquid  known  as  bisulphide  of  carbon  has  great  disper- 
sive power ;  hence  it  is  often  used  for  prisms.  When  a 
liquid  is  used  in  this  way,  it  is  enclosed  in  a  hollow  glass 
prism. 

In  order  to  obtain  a  spectrum  in  which  the  colors  are 
distinctly  seen,  the  opening  through  which  the  light  enters 
should  be  very  narrow,  and  if  the  refracting  angle  of  the 
prism  is,  as  usual,  60°,  the  screen  on  which  the  spectrum  is 
received  must  be  5  or  6  yards  distant. 


LIGHT.  107 

10 1.  Achromatic  Prism.  —  By   combining   a   flint-glass 
prism  CDF,  (Figure  75),  with  a  crown-glass  prism  C B  F, 
the  dispersive  power  of  the  latter  p. 

may  be  neutralized,  without  whol- 
ly neutralizing  its  refractive  pow- 
er. The  reason  of  this  will  be  evi- 
dent from  the  figure.  The  prism 
CDF,  in  order  to  have  the  same 
dispersive  power  as  C  B  F,  needs 
be  only  half  as  thick  as  the  latter ; 
so  that  the  edges  B  C  and  FD  are  still  inclined  as  though 
they  were  sides  of  the  larger  prism  A  B  F. 

Such  a  combination  of  prisms  forms  what  is  called  an 
achromatic  (colorless]  prism. 

102.  The  Prismatic  Colors  are  Simple.  —  If  all  the  colors 
of  the  spectrum  except  one  be  cut  off  by  a  screen,  and  that 
one  be  allowed  to  fall  on  a  second  prism,   as  shown  in 
Figure  76,  it  will  be  again  refracted,  but  will  not  be  sepa- 

Fig.  76. 


rated  into  different  colors.  Hence  the  colors  of  the  spec- 
trum are  said  to  be  simple. 

103.  The  Prismatic  Colors  are  unequally  Refrangible.  — • 
The  position  of  the  colors  in  the  spectrum  shows  that  they 
are  not  equally  refracted.  The  red  is  least,  and  the  violet 
most  refracted. 

That  the  colors  are  unequally  refrangible  may  be  shown 
by  the  following  experiment.  If  the  beam  of  light  S, 


LIGHT. 


(Figure  77,)  after  passing  through  the  horizontal  prism  A, 
be  allowed  to  fall  on  the  upright  prism  J3,  it  forms  the 

Fig.  77. 


oblique  spectrum  v'  r',  proving  that  from  red  to  violet  the 
colors  are  more  and  more  refrangible. 

104.  The  Composition  of  White  Light.  —  These  experi- 
ments with  the  prism  seem  to  show  that  white  light  is  not 
simple,  but  made  up  of  the  seven  prismatic  colors.  This 
view  is  confirmed  by  the  fact  that  white  light  can  be  pro- 
duced by  the  blending  of  these  seven  colors.  If  the  spec- 
trum produced  by  one  prism  be  allowed  to  fall  upon  a 
second  prism  exactly  like  the  first,  arranged  as  shown  in 

Figure  78,  the  latter  brings 
together  again  the  rays  which 
have  been  dispersed  by  the 
former,  and  white  light  is  the 
result. 

The  same  may  be  shown 
by  mixing  these  colors  in 
the  eye.  This  can  be  done  by  painting  them  in  the 
proper  proportions  upon  a  circular  disc  (Figure  79)  and 
making  this  disc  rotate  rapidly,  as  shown  in  Figure  80. 
The  impression  of  each  color  remains  in  the  eye  during  a 


LIGHT. 


I09 


complete  rotation  of  the  disc,  so  that  the  seven  are  blended 
into  one,  and  the  disc  appears  white. 


Fig.  79. 


Fig.  80. 


Fig.  81. 


White  light,  or  something  which  ordinary  eyes  cannot 
distinguish  from  it,  may  also  be  produced  by  the  blending 
of  a  part  of  the  prismatic  colors.  Thus  red,  yellow,  and 
blue,  or  red,  green,  and  blue,  will  form  white.  This  fact 
has  led  some  to  suppose  that  the  solar  spectrum  is  made  up 
of  but  three  simple  colors.  Brewster  chose  red,  yellow,  and 
blue.  He  assumed  that  each  one  of  these  colors  extended 
the  whole  length  of  the 
spectrum,  as  shown  in 
Figure  81.  The  height 
of  the  curve  shows  the 
intensity  of  each  color 
in  different  parts  of  the 
spectrum.  On  this  theory 
the  orange  is  produced  by  a  mixture  of  the  red  and 
yellow ;  the  green  by  a  mixture  of  the  yellow  and  blue ; 
and  so  on. 


110  LIGHT. 

But  it  has  been  shown  by  Maxwell  and  Helmholtz  that 
"  the  direct  mixture  of  the  prismatic  yellow  and  blue,  in 
whatever  proportion,  can  nohow  be  made  to  produce  green." 
If,  however,  we  take  red,  green,  and  blue  as  the  three  pri- 
mary colors,  all  the  colors  of  the  spectrum  can  be  produced 
by  mixing  these  in  different  proportions.  The  way  in 
Fig  82  which  these  three  col- 

ors must  be  distribut- 
ed through  the  spec- 
trum, in  order  to  give 
the  seven  prismatic 
colors,  is  shown  in 
Figure  82. 

105.  Complementary  Colors.  —  If  we  suppose  the  spectrum 
to  be  divided  into  any  two  parts,  and  the  colors  in  each  part 
mixed,  they  will  form  what  are  called  complementary  colors; 
that  is,  one  will  contain  what  the  other  needs  to  make 
white  light.  We  often  call  colors  complementary  when  their 
mixture  would  approach  more  or  less  nearly  to  white. 

SUMMARY. 

In  passing  through  a  prism  a  beam  of  white  light  is  dis- 
persed, and  forms  a  spectrum  of  seven  colors.  Different 
substances  disperse  light  differently.  Hence  two  prisms 
may  be  combined  so  as  to  form  an  achromatic  prism. 
(100,  101.) 

Prismatic  colors  are  simple  and  unequally  refrangible. 
(102,  103.) 

The  blending  of  the  seven  prismatic  colors  produces 
white  light. 

It  is  possible  to  form  the  solar  spectrum  out  of  the  three 
simple  colors,  red,  green,  and  blue.  (104.) 

Two  colors  whose  mixture  will  produce  white  light  are 
said  to  be  complementary.  (105.) 


LIGHT.  Ill 


ABSORPTION. 

106.  If  light  be  made  to  pass  through  a  piece  of  colored 
glass,  and  then  to  fall  upon  a  prism,  the  spectrum  will  be 
found  to  be  wanting  in  certain  colors.     If  red  glass  is  used, 
the  spectrum  will  contain  little  besides  red  light;  if  blue  or 
green  glass  is  used,  the  spectrum  will  be  rich  in  blue  or 
green,  and  deficient  in  other  colors.     A  part  of  the  light, 
then,  is  retained  in  the  glass,  and  is  said  to  be  absorbed  by 
it.     In  this  way  all  colored  transparent  bodies  are  found  to 
absorb  a  portion  of  the  light  which  falls  upon  them. 

107.  The  Color  of  Bodies.  —  Opaque  bodies,  as  well  as 
transparent  ones,  absorb  light.    This  explains  why  it  is  that, 
when  white  light  is  falling  upon  non-luminous  bodies,  they 
do  not  all  appear  of  the  same  color.     They  are  really  sift- 
ing the  light  which  they  receive,  absorbing  a  part  and  dif- 
fusing or  transmitting  the  rest.     Their  color  depends  upon 
the  light  which  they  reflect,  and  this  is  of  course  the  com- 
plement of  that  which  they  absorb.    Thus  a  body  which  ab- 
sorbs all  the  prismatic  colors  except  red  appears  red ;  one 
which  absorbs  all  except  green  appears  green ;  and  so  on. 
A  painter  does  not  add  color  to  his  canvas,  but  destroys  a 
part  of  its  color ;  that  is,  he  causes  it  to  absorb  a  part  of 
the  white  light  which  falls  upon  it,  and  to  reflect  only  the 
remainder,  instead  of  reflecting  it  all.     His  direct  action 
is  upon  the  tint  complementary  to  that  which  he  aims  to 
produce. 

It  sometimes  happens  that  bodies  transmit  a  color  differ- 
ent from  that  which  they  reflect,  and  such  bodies  appear 
of  a  different  color  according  as  they  are  seen  by  trans- 
mitted or  reflected  light.  This  is  the  case  with  gold,  which 
appears  yellow  by  reflected  light,  and  green  by  transmitted 
light,  as  may  be  seen  by  holding  a  piece  of  gold  leaf  be- 
tween the  eye  and  the  sunshine. 


112  LIGHT. 

1 08.  The  Analysis  of  Colors.  —  The  colors  of  objects 
may  be  analyzed  by  means  of  a  prism.     Take  a  very  nar- 
row strip  of  the  object,  a  mere  line  of  colored  light,  and 
place  it  upon  a  perfectly  black  ground  and  in  a  very  strong 
light.     Examine  this  strip  through  a  prism,  whose  edge  is 
held  parallel  with  it,  and  it  appears  dilated  into  a  spectrum, 
which  has  only  rays  of  those  colors  which  combine  to  form 
its  tint. 

A  cheap  and  convenient  instrument  for  this  analysis  may 
be  made  by  fastening  a  metal  plate,  having  in  it  a  sharply 
cut  and  very  narrow  slit,  to  one  end  of  a  tube  of  metal  or 
pasteboard,  about  an  inch  square  and  12  or  14  inches 
long,  and  blackened  within.  A  small  prism  of  colorless 
flint  glass  is  fixed  within  the  other  end  parallel  with  the 
slit,  so  that  when  the  tube  is  directed  to  a  white  cloud,  the 
slit  shall  be  seen  dilated  into  a  clear  prismatic  spectrurp 
The  object  to  be  examined  must  be  placed  so  near  the  slit 
as  to  allow  no  other  rays  to  enter  than  come  from  some 
part  of  its  surface,  and  must  be  strongly  illuminated  either 
by  direct  sunshine  or  by  means  of  a  lens. 

When  analyzed  in  this  way  all  natural  colors  are  found 
to  be  compound. 

109.  Spectrum  Analysis.  —  Let   us  now  analyze  more 
thoroughly  the  light  given  out  by  luminous  bodies.     We 
will  begin  with  colored  flames. 

If  a  piece  of  platinum  wire  be  dipped  in  a  solution  of 
soda,  and  held  in  the  colorless  flame  of  an  alcohol  lamp, 
or  a  Bunsen's  gas-burner,  the  flame  becomes  of  an  intense 
yellow.  This  color  is  due  to  the  heated  vapor  of  sodium 
in  the  flame.  If  we  dip  another  platinum  wire  in  a  solution 
of  lithium,  and  hold  it  in  the  colorless  flame,  a  rich  crim- 
son hue  is  imparted  to  the  flame.  The  vapor  of  copper 
colors  the  flame  green.  Other  metals  give  characteristic 
colors  to  the  flame. 

no.   The  Spectroscope. — These  colored   flames   can  be 


LIGHT. 


best  analyzed  by  means  of  the  spectroscope,  shown  in  Figure 
83.  The  light  from  the  flame  is  admitted  through  a  narrow 
slit  into  the  tube  B,  where  it  is  concentrated  by  lenses  and 


Fig.  83. 


thrown  upon  the  prism  P.  The  spectrum  formed  is  ex- 
amined with  the  telescope  A. 

When  the  spectrum  of  the  sodium  flame  is  thus  ex- 
amined, it  is  found  to  consist,  not  of  a  long  strip  of  colored 
light,  like  the  solar  spectrum,  but  of  a  single  bright  yellow 
line,  as  shown  at  III.  in  Plate  I.  When  other  flames 
colored  by  metallic  vapors  are  examined,  it  is  found  that 
their  spectra  in  all  cases  consist  of  bright  lines  separated 
by  dark  spaces.  In  Plate  I.,  II.  shows  the  spectrum  of 
potassium ;  IV.  the  spectrum  of  ccesium ;  and  V.  that  of 
rubidium. 

The  spectrum  of  each  substance  always  consists  of  the 
same  lines  in  the  same  relative  positions.  Hence  the  spec- 

H 


114  LIGHT. 

troscope  furnishes  a  ready  means  of  detecting  the  presence 
of  any  substance ;  for,  even  when  several  substances  are 
mixed,  each  gives  to  the  spectrum  the  characteristic  lines 
which  cannot  be  mistaken. 

This  method  of  detecting  a  substance  is  remarkable  for 
its  delicacy.  Thus,  a  portion  of  sodium  less  than  the 
—  of  a  grain  gives  to  the  spectrum  its  yellow  line. 
The  compounds  of  lithium,  which  were  formerly  supposed 
to  be  contained  in  only  four  minerals,  have  been  shown  by 
the  spectroscope  to  be  substances  of  very  common  occur- 
rence, being  found  in  minute  quantities  in  almost  all  spring 
waters,  as  well  as  in  tea,  tobacco,  milk,  and  blood.  We 
can  thus  detect  6o^000  of  a  grain  of  lithium. 

A  still  more  striking  proof  of  the  value  of  spectrum 
analysis  is  the  fact  that  several  new  metals  have  been  dis- 
covered by  this  means.  Among  these  are  ctesium  and 
rubidium,  the  spectra  of  which  are  shown  in  the  plate. 

in.  Gases  absorb  the  Same  Kind  of  Light  as  they  emit 
when  heated  to  Incandescence.  —  If  a  piece  of  lime  be  held  in 
a  flame  of  burning  oxygen  and  hydrogen,*  it  becomes  white 
hot,  and  gives  out  an  intense  light.  If  this  light  is  ex- 
amined with  the  spectroscope,  its  spectrum  is  seen  to  be 
an  unbroken  strip  of  colored  light,  or  a  continuous  spec- 
trum, as  it  is  called,  to  distinguish  it  from  the  spectrum  of 
a  gas,  which  is  made  up  of  bright  lines  separated  by  dark 
spaces.  If  this  lime  light  is  allowed  to  pass  through  the 
yellow  sodium  flame,  and  is  then  examined  with  the  spec- 
troscope, a  dark  line  is  seen  to  occupy  the  place  of  the 
yellow  line  of  the  sodium  spectrum.  This  must  be  due  to 
the  fact  that  the  sodium  vapor  has  absorbed  just  the  kind 
of  light  which  it  gives  out,  and  thus  caused  that  portion  of 
the  spectrum  to  be  comparatively  dark.  In  this  case  the 
sodium  spectrum  is  said  to  be  reversed.  In  like  manner 

*  See  the  "  Chemistry  "  of  the  "  Cambridge  Physics,"  §§  132,  185 


LIGHT.  115 

the  spectra  of  many  other  substances  have  been  reversed, 
each  substance  in  a  state  of  vapor  having  the  power  to 
absorb  the  same  rays  which  it  gives  out  when  heated  to  in- 
candescence. 

112.  Fraunhofer's  Lines.  —  When  the  light  of  the  sun  is 
examined  with  a  spectroscope,  it  is  found  that  the  spectrum 
is  crossed  by  a  great  number  of  dark  lines,  known  as 
Fraunhofer1  s  tines,  from  their  discoverer.  A  few  of  the 
stronger  ones  are  shown  at  I.  in  Plate  I.  The  only  satis- 
factory explanation  of  these  lines  is  that  the  white  light 
given  out  by  the  solid  or  liquid  mass  of  the  sun  is  partial- 
ly absorbed  by  vapors  in  his  atmosphere.  We  must  then 
have  in  the  solar  spectrum  the  reversed  spectra  of  the  sub- 
stances which  exist  in  that  atmosphere.  Strange  as  it  may 
seem,  we  have  then  in  the  spectroscope  a  means  of  analyz- 
ing the  atmosphere  of  the  sun.  We  have  only  to  find 
whether  the  dark  lines  in  the  solar  spectrum  correspond 
with  the  bright  lines  in  the  spectra  of  substances  known  to 
us.  Many  such  coincidences  have  been  detected,  and  we 
are  now  quite  certain  that  iron,  sodium,  magnesium,  cal- 
cium, chromium,  nickel,  barium,  copper,  zinc,  and  hydrogen 
exist  as  gases  in  the  atmosphere  of  the  sun. 

Nor  is  this  all.  The  spectra  of  the  stars  all  show  dark 
lines.  These  are  for  the  most  part  different  from  the  solar 
lines,  and  from  those  of  one  another.  Hence  we  conclude 
that  the  composition  of  the  solar  and  stellar  atmospheres 
is  not  the  same.  Many  of  the  substances  known  on  this 
earth  have  been  detected  in  the  atmosphere  of  the  stars 
by  Huggins  and  Miller,  to  whom  we  owe  this  important 
discovery.  The  star  known  as  Aldebaran  has  in  its  at- 
mosphere hydrogen,  sodium,  magnesium,  calcium,  iron,  tel- 
lurium, antimony,  bismuth,  and  mercury ;  while  in  the  at- 
mosphere of  Sirius  only  sodium,  magnesium,  and  hydro- 
gen have  with  certainty  been  detected. 


Il6  LIGHT. 


SUMMARY. 

Different  bodies  absorb  light  of  different  colors.  It  is 
the  sifting  of  the  rays  of  light  by  absorption  which  gives 
bodies  their  color.  (106.  107.) 

The  color  of  bodies  may  be  analyzed  by  means  of  a 
prism.  (108.) 

Different  substances  emit  light  of  different  colors. 
(109.) 

Incandescent  gases  give  dark  spectra  crossed  by  bright 
lines. 

The  presence  of  any  substance  in  the  flame  can  be  de- 
tected by  means  of  the  spectroscope,  (no.) 

By  means  of  the  lime  or  magnesium  light,  the  spectra  of 
the  elements  may  be  reversed,  since  a  substance  absorbs 
readily  those  rays  which  it  can  emit,  (m.) 

Solar  and  stellar  spectra  are  crossed  by  dark  lines, 
known  as  Fraunhofer's  lines.  These  are  due  to  absorption. 

The  composition  of  the  atmosphere  of  the  sun  and  stars 
may  be  ascertained  by  analyzing  their  light.  (112.) 

INTERFERENCE  AND  THE  UNDULATORY  THEORY  OF 
LIGHT. 

113.'  Colors  of  Soap-Bubbles*  —  If  a  soap-bubble  be 
blown  in  a  clear  circular  saucer,  so  as  to  be  somewhat 
more  than  hemispherical,  and  then  be  placed  under  a 
glass  cover  to  keep  it  from  gusts  of  air,  the  colors  which  in 
the  blowing  had  wandered  irregularly  over  its  surface  will 
gather  into  'regular  concentric  rings  at  its  top.  If  the 
bubble  be  a  thick  one,  only  faint  colors  will  appear  at 
first ;  but  they  will  gradually  grow  more  vivid.  Each  color, 
however,  does  not  become  brighter,  but  spreads  away,  and 
a  new  and  richer  one  takes  its  place.  In  this  way  the 

*  See  Appendix,  TV. 


LIGHT.  1 1  7 

rings  go  on  increasing  in  number  and  brilliancy,  until  at 
length  a  very  clear  white  spot  appears  at  the  top,  and  is 
quickly  followed  by  a  perfectly  black  one.  Soon  after  this 
the  bubble  bursts.  During  all  this  time  the  bubble  has 
been  gradually  becoming  thinner"  by  the  slow  running  down 
of  the  liquid  from  the  top.  The  ring-like  arrangement  of 
the  colors  around  the  thinnest  part  of  the  bubble  as  a 
centre  seems  to  show  that  the  tint  depends  upon  the  thick- 
ness of  the  liquid  film  at  the  point  where  the  color  ap- 
pears ;  a  certain  tint  being  developed  at  a  certain  thickness 
and  at  no  other.  The  order  of  the  colored  rings  and  of 
the  tints  in  them  is  always  the  same,  after  the  black  central 
spot  has  once  formed.  None  of  these  tints  are  pure  pris- 
matic colors.  To  see  them  to  the  best  advantage  the  bub- 
ble must  be  illumined  by  diffused  light,  not  by  direct  sun- 
light. 

If  the  bubble  is  illumined  by  letting  the  colors  of  the 
spectrum  fall  upon  it  one  by  one,  when  the  red  light  falls 
upon  it  the  rings  will  appear  all  red,  separated  by  black 
spaces ;  when  the  yellow  light  falls  upon  it,  they  will  be 
yellow  with  black  spaces  ;  and  so  on  for  all  the  colors.  In 
all  cases  the  rings  are  more  numerous  than  when  the  bub- 
ble is  illumined  by  white  light,  but  the  diameter  and  breadth 
of  the  rings  vary  with  the  color  used,  being  greatest  for 
the  red  and  least  for  the  violet. 

This  explains  the  composite  colors  of  the  rings  when 
white  light  is  used ;  for  in  this  case  we  have  the  rings  of 
the  seven  colors  overlapping  one  another  in  various  ways 
so  as  to  produce  a  variety  of  tints. 

114.  These  Colors  do  not  depend  upon  the  Liquid  of  which 
the  Bubble  is  made.  —  What  now  is  the  cause  of  these 
colored  rings?  They  do  not  depend  on  the  material  of 
which  the  bubble  is  made,  for  a  film  of  any  substance 
whatever  will  produce  them,  if  it  be  thin  enough.  They 
are  seen  in  the  oily  scum  upon  stagnant  water ;  in  the 


Il8  LIGHT. 

gayly  painted  wings  of  insects  ;  and  even  on  polished  steel. 
Bubbles  may  be  blown  with  a  variety  of  liquids  and  even 
of  glass,  and  they  all  display  the  same  hues  in  the  same 
order.  In  fact  it  requires  no  medium  at  all  to  produce 
them,  but  only  an  interval  between  two  reflecting  surfaces. 
They  are  seen  in  a  crack  which  does  not  extend  complete- 
ly through  a  thick  piece  of  glass,  and  in  mica  when  two 
of  its  layers  are  partially  separated.  It  may  be  said  that 
there  is  air  between  the  surfaces ;  but  under  the  exhausted 
receiver  of  an  air-pump  the  rings  remain  unchanged. 

115.  These  Colors  are  due  to  Interference.  —  It  is,  then,  to 
the  interval  between  the  reflecting  surfaces  that  we  are  to 
look  for  the  origin  of  these  colors.     A  part  of  the  light  will 
of  course  be  reflected  at  each  surface,  and  the  rays  reflected 
from  both  will  take  very  nearly  the  same  direction.     When 
simple  or  homogeneous  light,  as  it  is  called,  is  allowed  to  fall 
on  the  bubble,  the  colored  rings,  as  we  have  seen,  are 
separated  by  dark  spaces.     At  certain  distances  between 
the  surfaces,  then,  the  rays  of  light  reflected  from  them 
destroy  each  other,  and  produce  darkness ;  while  at  other 
distances  they  combine  and  produce  more  intense  light, 
Since  the  rings  of  the  more  refrangible  colors  are  narrower, 
it  follows  that  the  distances  at  which  the  rays  of  these  col- 
ors destroy  each  other  are  less  than  for  the  less  refrangible 
rays.     The  rays  which  destroy  each  other  are  said  to  in- 
terfere,  and    the   colored    rings   are  evidently  due    to   in- 
terference. 

1 1 6.  The  Undulatory  Theory  of  Light. — We  have  now 
seen  that  rays  of  light  are  reflected,  are  refracted,  and  in- 
terfere in  the  £ame  way  as  those  of  sound.     It  seems  prob- 
able, then,  that  both  light  and  sound  are  propagated  in  the 
same  way.      We  have  seen  that  sound  is  propagated  by 
means  of  waves,  and  it  is  therefore  probable  that  light  is 
propagated  by  waves.     We  have  seen,  too,  that  sounds  in- 
terfere with  each  other  so  as  to  produce  silence,  when  their 


LIGHT.  119 

waves  meet  in  opposite  phases  (36) ;  and  from  the  way  in 
which  sounds  interfere  we  should  be  driven  to  conclude 
that  sound  is  propagated  by  waves,  even  if  we  did  not 
know  the  fact  already.  Do  the  rays  of  light  interfere  in 
such  a  way  as  to  show  that  light  is  propagated  by  waves  ? 

117.  When  Light  is  reflected  from  the  Surface  of  a  Rarer 
Medium,  the  Phase  of  the  Wave  is  Changed.  —  We  have  seen 
in  the  soap-bubble  that  as  the  top  becomes  very  thin  it  ap- 
pears black,  and  the  blackness  grows  more  intense  until 
the  thickness  becomes  nothing,  and  the  bubble  bursts. 
Just  before  it  bursts,  the  two  surfaces  of  the  film  are  virtu- 
ally together,  and  the  rays  reflected  from  them  must  there- 
fore start  back  together ;  and  it  would  seem  that  they 
should  produce  light  instead  of  darkness,  —  that  is,  that 
their  phases  should  coincide  rather  than  interfere, — if 
light,  like  sound,  is  really  propagated  by  waves. 

This  interference,  then,  seems  at  first  inconsistent  with 
the  wave  theory  of  light.  The  following  illustration  of 
Herschel's,  however,  will  show  how  it  is.  reconciled  with 
that  theory.  Imagine  a  number  of  ivory  balls  all  of  a  size 
placed  in  a  row,  in  contact  with  one  another,  but  con- 
nected only  by  a  rubber  cord  which  runs  through  them  all 
and  is  fastened  at  the  centre  of  each.  Let  an  ivory  ball  of 
exactly  the  same  size  be  driven  against  the  end  of  the  row. 
According  to  the  law  of  the  collision  of  elastic  bodies,  this 
ball  will  give  up  all  its  motion  to  the  one  it  strikes,  and  this 
to  the  next,  and  so  on  to  the  end  of  the  row.  None  of  the 
balls  move  except  the  last,  but  they  are  all  made  to  press 
against  one  another,  ar\4  a  wave  of  compression  may  be  said 
to  run  along  the  line.  The  last  ball  has  nothing  to  which 
to  give  its  motio^  and  therefore  starts  off;  but  it  is  quickly 
checked  and  drawn  back  by  the  elasticity  of  the  rubber 
cord.  But  at  the  same  time  it  pulls  the  next  ball  forward, 
and  this  the  next,  and  so  on  to  the  end  of  the  line.  In 
this  way  a  wave  of  extension  runs  back  along  the  row. 


120  LIGHT. 

Here  then  the  direct  wave  changes  its  phase  on  being 
reflected.  This  is,  however,  an  extreme  case,  and  unlike 
anything  which  we  find  in  the  transmission  of  light ;  for 
when  it  passes  from  one  medium  into  another  there  are  al- 
ways particles  beyond  to  which  the  moving  particles  can 
impart  their  motion.  Let  us  now  suppose  that  there  is  a 
second  row  of  smaller  elastic  balls,  near  the  end  of  the 
first,  and  arranged  exactly  in  the  same  way ;  and  that  at 
the  end  of  the  first  there  is  a  detached  ball  of  the  same 
size  as  those  in  the  second  row.  The  line  of  larger  balls 
will  represent  the  condition  of  the  particles  of  a  denser 
medium  in  contact  with  those  of  a  rarer  one.  Let  now  an 
impulse  be  sent  along  the  row  of  larger  balls,  as  at  first. 
The  last  ball  of  the  line  drives  the  detached  ball  off  against 
the  first  ball  of  the  second  row,  and  thus  sends  forward  a 
wave  of  compression.  But  the  smaller  ball  will  not  carry 
off  all  the  motion  of  the  larger  one,  which  will  also  ad- 
vance till  it  is  checked  by  the  rubber  cord.  While  this 
ball  is  drawn  back  it  draws  forward  the  ball  behind  it, 
and  this  the  next,  and  so  on.  In  this  case,  part  of  the 
wave  is  reflected,  and  in  an  opposite  phase  from  the  direct 
wave. 

If  the  balls  in  the  first  row  are  smaller  than  the  detached 
ball  and  those  in  the  second  row,  they  will  represent  the 
condition  of  the  particles  of  a  rarer  medium  in  contact 
with  those  of  a  denser  one.  If  an  impulse  be  sent  along 
the  first  line,  as  before,  the  detached  ball  will  not  only 
move  forward,  but  also  cause  the  ball  behind  it  to  rebound. 
Here  the  reflected  wave  has  the  same  phase  as  the  direct 
one. 

When,  therefore,  a  wave  is  reflected  from  a  rarer  me- 
dium, it  changes  its  phase  ;  but  not  when  reflected  from  a 
denser  medium. 

We  see,  then,  that  the  fact  that  the  top  of  the  bubble  is 
black  is  not  an  objection  to  the  theory  that  light  is  propa- 


LIGHT.  I  2  I 

gated  by  waves  ;  for  at  the  outer  surface  of  the  bubble  the 
rays  of  light  are  reflected  from  a  denser  medium,  while  at 
the  inner  surface  they  are  reflected  from  a  rarer  medium, 
and  they  should  therefore  start  back  in  opposite  phases 
when  the  surfaces  are  together. 

1  1  8.  When  Homogeneous  Light  is  used,  the  Distance  be- 
tween the  Reflecting  Surfaces  at  the  second,  third,  and  fourth 
Dark  Rings  if  twice,  thrice,  and  four  times  that  at  the  first, 
and  so  on.  —  If  the  dark  rings  are  due  to  the  meeting  of 
waves  of  opposite  phases,  the  distance  between  the  reflect- 
ing surfaces  at  the  second  ring  should,  when  homogeneous 
light  is  used,  be  twice  as  great  as  at  the  first  ;  at  the  third, 
thrice  as  great  as  at  the  first  ;  and  so  on.  For  at  the  first 
ring  the  light  reflected  from  the  inner  surface  must  travel 
over  a  distance  of  a  wave-length  more  than  that  reflected 
from  the  outer  surface,  in  order  that  the  waves  may  meet 
in  the  opposite  phase  ;  and  at  the  second  ring  it  must 
travel  over  the  length  of  two  waves  more  ;  at  the  third 
ring,  over  the  length  of  three  waves  more  ;  and  so  on.  Is 
this  the  case  ? 

The  thickness  of  the  soap-bubble  at  the  different  points 
cannot  be  directly  measured  ;  but  we  have  seen  that  the 
rings  can  be  obtained  by  other  means.  The  following 
arrangement  enables  us  readily  to  measure  the  distance 
between  the  reflecting  surfaces. 

Upon  a  perfectly  flat  and  smooth  plate  of  glass  is  placed 
another  piece  equally  smooth,  but  with  its  under  surface 
slightly  curved,  as  shown  in  Figure  84.  This  curved  sur- 
face should  be  a  portion  of  the 

r  r  j-  Fig.  84. 

surface  of  a  sphere  whose  radius' 


n    nr    Cn    fppf        Whfn 

^       ^*-         0  1*-'V^L.  »»    li^ll 

this  curved  glass  is  pressed  firm- 

ly down  upon  the  plate,  the  centre  appears  black,  and  is 
surrounded  by  colored  rings  (Figure  85),  as  in  the  soap- 
bubble.     Suppose  that  homogeneous  light  of  some  color, 
6 


122 


LIGHT. 


Fig.  85. 


as  red,  be  allowed  to  fall  perpendicularly  upon  the  upper 
glass.  Dark  rings  will  be  formed  at  i,  2,  3, 
and  4  (Figure  86),  and  the  diameters  i  i, 
2  2,  etc.  of  these  rings  can  be  easily  meas- 
ured. They  are  always  found  to  be  in  the 
proportion  of  i,  1.414.  1.732,  2.000,  and  so 
on.  Now  these  numbers  are  the  square 
roots  of  the  numbers 
i,  -2,  3,  4,  and  so  on  ; 
and  we  know  from 
the  form  of  the  sphere 
that  the  distances  i  £, 
2  c,  3  d,  4  ^,  etc.  are 
to  one  another  as  the 
-squares  of  the  chords 
i  i,  2  2,  3  3,  4  4,  etc. 
Hence  the  distance 
between  the  reflecting 
surfaces  at  the  second 
dark  ring  is  twice 
that  at  the  first,  and 
so  on. 

119.  Light  is  prop- 
agated by  means  of  the  Ether.  —  We  have  now  seen  that 
light  interferes  in  such  a  way  as  to  show  that  it  is  prop- 
agated by  waves.  If,  however,  a  lighted  lamp  be  placed 
behind  the  receiver  of  an  air-pump,  and  the  air  be  exhaust- 
ed, the  flame  still  shines  through  the  receiver,  showing  that 
light  is  not  propagated  by  means  of  the  air,  as  is  the  case 
with  sound.  We  know  also  that  the  heavenly  bodies  are 
far  beyond  the  limits  of  the  earth's  atmosphere,  which  ex- 
tends to  a  height  of  only  about  50  miles. 

We  must  therefore  conclude  that  all  space  is  filled  with 
an  elastic  medium  through  which  the  light-waves  are  prop- 
agated as  the  sound-waves  are  sent  through  the  air. 


LIGHT. 


I23 


This  medium  is  called  the  ether,  and  it  fills  not  only  the 
spaces  between  the  heavenly  bodies,  but  also  those  be- 
tween the  molecules  of  all  substances.  It  cannot  be  ex- 
hausted from  a  receiver,  since  it  readily  passes  through  the 
glass. 

120.  The  Length  of  the  Light-  Wave,  —  We  have  seen  that 
the  light  reflected  from /"(Figure  86)  must  travel  a  wave- 
length farther  than  that  reflected  from  i,  in  order  that 
the  waves  reflected  from  these  points  may  meet  in  oppo- 
site phases,  and  so  give  a  dark  ring.  Now  the  wave  re- 
flected from  f  must  evidently  travel  over  the  space  if 
twice  :  hence  i/"must  be  J  the  length  of  a  luminous  wave, 
and  we  have  seen  that  this  is  J  of  4  /.  Now  we  can  easily 
find  the  length  of  4  /.  4  m  is  half  the  diameter  of  the 
fourth  bright  ring,  and  can  be  found  by  measurement.  We 
know  the  length  of  the  radius  4  C,  and  4  m  C  is  a  right-an- 
gled triangle.  In  this  triangle  we  know  the  length  of  the 
hypothenuse  4  C,  and  of  the  side  4  m.  Hence  we  can  find 
the  length  of  C  m.  The  radius  C  a  —  Cm  =  am^=^i. 

In  this  way  the  lengths  of  the  waves  of  light  of  the  differ- 
ent colors  have  been  found.  The  following  table  shows 
the  lengths  of  these  waves,  and  also  the  number  that  enter 
the  eye  in  a  second  :  — 


Colors 

Length  of  waves 
in  parts  of  an  inch. 

Number  of 
waves  in  an 
inch. 

Number  of  waves  in  a 
second. 

Extreme  Red 

.0000266 

37,640 

458,OOO,OOO,OOO,OOO 

Red 
Orange 

.0000256 
.0000240 

39,l8o 
4I,6lO 

477,000,000,000.000 
506,000,000,000,000 

Yellow 

.OOOO227 

44,000 

535,OOO,OOO,OOO,OOO 

Green 

.0000211 

47,460 

577,  ooo,  ooo,  ooo,  ooo 

Blue 

.0000196 

51,110 

622,000,000,000,000 

Indigo 

.OOOOI85 

54»o7o 

658,000,000,000,000 

Violet 

.0000174              57.49° 

699,000,000,000,000 

Extreme  Violet 

.0000167           59>75° 

727,000,000,000,000 

According  to  Eisenlohr  the  length  of  the  waves  in  the  ex- 


1 24  LIGHT. 

treme  red  ray  is  just  double  the  length  of  the  waves  in  the 
invisible  rays  beyond  the  violet.  The  whole  range  of  rays, 
then,  extends  only  over  what  is  equivalent  to  a  single 
octave  in  music. 

121.  The  Origin  of  Light.  —  We  have  now  seen  that 
light,  as  well  as  sound,  is  propagated  by  waves  in  an  elas- 
tic medium,  and  that  sound  originates  in  vibrations  of  the 
particles  of  the  sounding  body.  It  is  very  probable,  then, 
that  light  also  has  its  origin  in  the  vibrations  of  the  par- 
ticles of  a  luminous  body.  In  ordinary  combustion,  which 
is  the  most  familiar  source  of  light,  the  atoms  of  the  oxygen 
in  the  air  are  rushing  into  combination  with  the  atoms  of 
the  burning  body  ;  and  the  collision  of  these  atoms  will 
be  very  likely  to  set  them  vibrating.  These  vibrations 
will  be  communicated  to  the  atoms  of  the  surrounding 
ether,  and  by  these  transmitted  to  the  eye.  The  color  of 
the  light  depends  on  the  rapidity  of  the  vibrations. 

The  particles  of  certain  substances  seem  to  be  capable 
of  vibrating  in  all  periods,  and  thus  of  producing  white 
light ;  while  those  of  other  substances  seem  to  be  capable 
of  vibrating  only  in  particular  periods,  and  therefore  they 
produce  light  of  different  colors.  It  is  seldom,  however, 
that  the  vibrations  of  the  molecules  are  limited  to  one 
period,  and  therefore  that  a  luminous  body  gives  out  homo- 
genous light.  We  can  now  understand  how  it  is  that  we 
can  detect  certain  substances  by  the  light  they  give.  Their 
particles  can  vibrate  only  in  certain  ways,  and  they  of  course 
cause  the  particles  of  ether  nearest  them  to  vibrate  in  the 
same  way.  The  vibrations  are  sent  on  unchanged  from 
particle  to  particle  of  the  ether,  and  are  ready  at  any  point 
to  reveal  the  nature  of  the  substance  in  which  they  origi- 
nated. The  vibrations  are  so  minute  that  it  would  seem 
impossible  to  find  out  their  character,  but  the  spectroscope 
enables  us  to  do  this  with  ease  and  accuracy. 

When  a  number  of  strings  of  different  lengths  and  ten- 


LIGHT.  125 

sion  are  stretched  in  the  air,  as  in  the  ^olian  harp,  they 
absorb  all  the  vibrations  accordant  to  their  own  which  fall 
upon  them,  while  they  allow  all  the  discordant  ones  to 
pass  on.  In  much  the  same  way  we  must  imagine  the 
molecules  of  a  body  suspended  in  the  ether,  from  which 
they  absorb  all  accordant  vibrations  while  they  transmit  all 
discordant  ones. 

Transparency  is  then  synonymous  with  discordance,  and 
opacity  with  accordance.  This  explains  the  fact  that  dif- 
ferent substances  absorb  light  of  different  colors,  and  also 
the  fact  that  incandescent  gases  give  out  light  of  the  same 
color  as  that  which  they  absorb. 

122.  Diffraction  Fringes.  —  Take  a  glass  lens  whose 
focal  length  is  about  an  inch,  and  let  a  beam  of  sunlight 
fall  upon  it  in  a  darkened  room.  The  light  will  be  con- 
centrated into  a  very  small  image  of  the  sun  about  an  inch 
from  the  lens,  and  will  then  diverge  from  it  in  a  luminous 
cone,  and  may  be  received  upon  a  screen.  Place  any  small 
opaque  body  within  this  cone  of  light,  so  that  it  may  cast 
a  shadow  upon  the  screen.  This  shadow,  instead  of  being 
sharply  denned,  as  we  should  expect  (85),  is  somewhat 
larger  than  it  should  be,  and  is  surrounded  by  three  colored 
fringes,  the  outer  one  being  extremely  faint.  If  homoge- 
neous light  is  used,  instead  of  the  fringes  we  get  bright 
rings  separated  by  dark  spaces,  the  breadth  of  the  rings 
varying  with  the  color  of  the  light.  When  white  light  is 
used,  these  different  sets  of  colored  rings  blend  so  as  to 
produce  the  fringes. 

If  the  opaque  body  is  long  and  very  narrow,  as  a  hair  or 
a  very  thin  strip  of  card,  besides  the  colored  fringes  al- 
ready described,  others  are  seen  within  the  shadow,  paral- 
lel to  its  length,  and  similarly  arranged  on  the  two  sides  of 
a  central  white  line. 

When  light  is  transmitted  through  a  very  narrow  slit,  the 
fringes  become  even  more  curious  and  complicated. 


126 


LIGHT. 


Fig.  87. 


To  see  these  diffraction  fringes  to  the  best  advantage,  a 

magnifying  glass  should  be  used,  putting  the  eye  in  place 

of  the  screen.* 

123.  Diffraction  Fringes  are  produced  by  Interference. — 

Diffraction  fringes  are  fully  explained  by  the  interference  of 
light,  according  to  the  undulatory 
theory.  Suppose  a  b  (Figure  87) 
to  be  a  portion  of  a  wave  of  light. 
Every  particle  of  ether  along  this 
curve  is  a  centre  of  a  set  of  waves, 

which  tend  to  run  not  only  forward  but  sideways  as  well. 

But   as  each  particle  Fig  88 

sends  equal  waves  in 

opposite  directions  at 

the  same  instant,  the 

lateral  waves  destroy 

one     another  ;    while 

the  advancing  portions 

unite  to  form  one  con- 
tinuous wave.    When, 

dowever,     the     wave 

rtieets  an  opaque  body 

/Figure  88),  the  par- 
dele  of  ether  nearest 

the  edge  of  the  opaque 

body,  since  there  are 

vibrating  particles  on 

only  one   side   of  it, 

can  start  a  new  set  of 

waves.     These  waves 

meet      the      original 

waves  in   opposite   phases  at  the  points  marked   by  the 

little  circles ;  in  the  same  phases  at  the  points  marked 

by  the  crosses.      They  of  course  interfere  in  the  former 

*  See  Appendix,  V. 


LIGHT 


case  and  coincide  in 
the  latter,  and  thus 
give  rise  to  the  colored 
fringes. 

If  the  opaque  body  is 
narrow,  as  shown  in 
Figure  89,  the  waves 
which  start  up  at  each 
edge  of  it  interfere  and 
coincide  behind  it,  so  as 
to  produce  the  interior 
fringes  and  the  central 
bright  line.  That  these 
interior  fringes  are  due 
to  the  interference  of 
the  waves  which  thus 
bend  round  the  edges 
of  the  opaque  body  is 
clearly  shown  by  their 
disappearance  when  the 
light  is  cut  off  from  one 
edge  by  a  screen. 


SUMMARY. 

Soap-bubbles  and  other  thin  films,  when  exposed  to 
light,  exhibit  colored  rings.  (113.) 

These  rings  are  always  seen  when  light  is  reflected  from 
two  surfaces  separated  by  a  very  small  interval.  (114.) 

They  are  caused  by  interference.     (115.) 

Light,  like  sound,  is  propagated  by  means  of  waves. 
(116.) 

When  light  is  reflected  from  the  surface  of  a  rarer  me- 
dium, the  phase  of  its  wave  is  changed.  (117.) 

Light  is  propagated  by  means  of  the  ether,     (i  19.) 


LIGHT. 


The  length  of  the  luminous  waves  can  be  found  by 
means  of  interference  rings.  (120.) 

Light  has  its  origin  in  the  vibrations  of  the  molecules  of 
a  luminous  body. 

The  molecules  of  a  body  are  usually  capable  of  vibrating 
in  several  periods.  Hence  a  luminous  body  seldom  gives 
out  homogeneous  light. 

A  body  absorbs  such  vibrations  as  are  accordant  with 
those  of  its  own  molecules,  and  reflects  or  transmits  such 
as  are  discordant.  (121.) 

When  small  bodies  are  seen  in  divergent  light,  they 
appear  surrounded  by  colored '  fringes,  called  diffraction 
fringes.  (122.) 

These  fringes  are  caused  by  interference.     (123.) 

DOUBLE  REFRACTION  AND  POLARIZATION. 

124.  Uniaxial  and  Biaxial  Crystals. — We  have  now 
seen  that  a  beam  of  ordinary  light  is  an  assemblage  of 
minute  vibrations  of  different  periods,  and  we  have  studied 
somewhat  the  effect  of  a  transparent  uncrystalline  body  on 
such  a  beam.  We  will  next  study  the  effect  of  transparent 
crystals  on  the  same.  We  will  select  for  this  purpose  a 
crystal  of  Iceland  spar  (crystallized  carbonate  of  lime). 
Such  a  crystal  is  shown  in  Figure  90.  A  crystal  of  this 
Fig  shape  is  called  a  rhomb.  It  has 

six  faces,  which  are  equal  par- 
allelograms. These  parallelo- 
grams are  so  arranged  that  three 
of  them  have  one  of  their  ob- 
tuse angles  at  a ;  and  the  other 
three,  one  of  their  obtuse  an- 
gles at  b.  The  parts  of  the  crystal  are  therefore  arranged 
symmetrically  about  the  line  a  b,  which  is  called  the  axis 
of  the  crystal. 


LIGHT.  129 

If  now  a  ray  of  light  be  allowed  to  fall  on  one  face  of 
this  crystal  in  a  darkened  room,  it  will  be  divided  into  two 
rays.  One  of  these  rays  is  found  to  conform  to  the  law  of 
ordinary  refraction,  and  is  therefore  called  the  ordinary 
ray.  The  other  ray  does  not  lie  in  the  same  plane  as  the 
incident  and  the  ordinary  rays,  and  does  not  conform  to 
the  law  of  sines  (93).  It  is  therefore  called  the  extraordi- 
nary ray.  By  cutting  parallel  plates  from  a  rhomb  of  Ice- 
land spar  in  various  directions,  it  is  found  that,  when  the 
plates  are  cut  perpendicularly  to  the  axis  of  the  crystal, 
they  will  allow  a  ray  of  ordinary  light  to  pass  through  them 
perpendicularly  without  dividing  it  into  two  parts ;  but  this 
is  true  of  plates  cut  in  no  other  direction.  In  other  words, 
a  ray  of  light  which  passes  through  a  rhomb  of  Iceland 
spar  parallel  to  its  axis  is  not  doubly  refracted ;  while  every 
ray  which  passes  through  it  in  a  different  direction  is 
thus  refracted.  For  this  reason  the  axis  of  the  crystal  is 
also  called  its  optical  axis.  The  ordinary  and  extraordi- 
nary rays  separate  most  widely  when  they  pass  through 
the  crystal  perpendicularly  to  its  optical  axis. 

In  many  crystals,  as  saltpetre  and  mica,  there  are  two 
directions  in  which  light  may  pass  through  them  without 
being  doubly  refracted.  Such  crystals  have  two  optical 
axes  and  are  called  biaxial  crystals,  to  distinguish  them 
from  uniaxial  crystals,  which  have  only  one  such  axis. 

When  a  ray  of  light  passes  through  a  biaxial  crystal  in 
such  a  direction  as  to  be  doubly  refracted,  both  rays  are 
usually  extraordinary  rays. 

125.  The  Double-refracting  Prism.  —  Since  the  opposite 
faces  of  a  rhomb  of  Iceland  spar  are  parallel,  the  ordinary 
and  extraordinary  rays  emerge  from  the  crystal  parallel  to 
the  incident  ray  and  to  each  other,  but  quite  near  together. 
If,  however,  the  crystal  be  cut  into  the  form  of  a  prism  in 
such  a  way  that  its  refracting  edge  may  be  parallel  to  the 
optical  axis,  the  ordinary  and  extraordinary  rays,  after  leav- 


130 


LIGHT. 


ing  the  prism,  will  diverge,  so  that  we  may  easily  insulate 
either  and  examine  it  separately.  Such  a  prism  will  of 
course  disperse  both  rays  so  as  to  produce 
spectra,  but  it  may  be  rendered  sufficiently 
achromatic  by  combining  with  it  a  second 
prism  of  glass,  whose  dispersive  power  is 
different  from  that  of  the  crystal.  This 
prism  is  usually  mounted  as  shown  in  Fig- 
ure 91. 

126.  The  Ordinary  and  Extraordinary  Rays  are  both 
Polarized.  —  If  a  beam  of  ordinary  light  be  allowed  to  fall 
on  a  double-refracting  prism,  and  the  extraordinary  ray  be 
cut  off  by  a  screen,  and  the  ordinary  ray  be  allowed  to  fall 
on  a  second  similar  prism  whose  refracting  edge  is  held 
parallel  to  that  of  the  first,  it  will  be  refracted  singly  and 
ordinarily.  If  the  refracting  edge  of  the  second  prism  be 
held  perpendicular  to  that  of  the  first,  the  ray  will  be  re- 
fracted singly  but  extraordinarily.  In  every  intermediate 
position,  it  will  be  doubly  refracted,  more  of  the  light  pass- 
ing into  the  ordinary  or  the  extraordinary  ray  according  to 
the  inclination  of  the  edges  of  the  two  prisms.  At  an  incli- 
nation of  45°,  the  light  is  equally  divided  between  the  two  ; 
in  passing  from  45°  to  90°,  more  and  more  of  the  light 
passes  into  the  extraordinary  ray;  from  45°  to  o°,  more  and 
more  into  the  ordinary  ray. 

If  the  ordinary  ray  be  cut  off,  and  the  extraordinary  ray 
be  allowed  to  fall  on  the  second  prism,  it  will  be  refracted 
singly  and  extraordinarily  when  the  edges  of  the  prisms 
are  parallel ;  singly  and  ordinarily  when  the  edges  are 
perpendicular ;  doubly  in  every  other  position. 

If  the  ordinary  ray  be  allowed  to  fall  upon  a  flat  plate 
of  tourmaline  whose  faces  are  cut  parallel  to  the  optical 
axis,  it  will  be  found,  when  the  plate  is  held  in  a  certain 
position,  that  the  ray  is  wholly  absorbed  ;  but  when  the 
plate  is  turned  round  from  this  position,  a  part  of  the 


LIGHT.  131 

ray  begins  to  be  transmitted  ;  and  when  it  has  been  turned 
through  90°,  the  whole  ray  is  transmitted. 

If  the  extraordinary  ray  be  allowed  to  fall  on  the  tour- 
maline, it  will  be  wholly  transmitted  where  the  ordinary 
ray  was  wholly  absorbed,  and  absorbed  where  that  was 
transmitted. 

If  the  ordinary  ray  be  allowed  to  fall  on  a  smooth  plate 
of  glass  at  an  angle  of  incidence  of  56^°,  it  is  found  that, 
when  the  plate  is  held  in  a  certain  position  with  reference 
to  the  ray,  it  will  be  wholly  reflected.  On  turning  the  glass 
round,  keeping  the  angle  of  incidence  unchanged,  the  ray 
begins  to  be  partly  transmitted,  and  when  the  glass  has 
been  turned  through  90°  it  is  wholly  transmitted.  If  the 
extraordinary  ray  be  used,  it  will  be  transmitted  where 
the  ordinary  ray  is  reflected,  and  reflected  where  that  is 
transmitted. 

The  above  experiments  show  that  both  the  ordinary  and 
extraordinary  rays  are  different  on  different  sides.  When 
the  prism  of  Iceland  spar  was  turned  round  through  90°, 
the  ray  which  had  been  at  first  refracted  ordinarily  was 
refracted  extraordinarily.  When  the  tourmaline  was  turned 
round  through  90°,  the  ray  which  had  been  absorbed  was 
transmitted.  .  When  the  glass  plate  was  turned  round 
through  90°,  the  ray  which  had  been  reflected  was  trans- 
mitted. 

Both  rays,  then,  have  acquired  sides,  so  to  speak ;  and 
the  corresponding  sides  of  the  two  rays  are  at  right  angles 
to  each  other.  In  other  words,  the  extraordinary  ray  is 
like  the  ordinary  ray  turned  round  through  90°. 

Light  which  has  thus  acquired  sides  is  said  to  be  polar- 
ized. The  ordinary  ray  is  said  to  be  polarized  in  a  plane 
parallel  to  the  optical  axis  of  the  crystal ;  and  the  extraor- 
dinary ray  in  a  plane  at  right  angles  to  that  axis. 

127.  The  Explanation  of  Polarization  and  Double  Refrac- 
tion. —  We  have  now  seen  that  both  light  and  sound  are 


I32 


LIGHT. 


propagated  by  vibrations,  and  that  a  ray  of  light  when  po- 
larized has  acquired  sides.  In  a  sound-wave,  the  particles 
are  vibrating  to  and  fro  in  the  direction  in  which  the  wave 
is  advancing,  and  it  is  therefore  difficult  to  imagine  how  a 
ray  of  sound  can  have  sides.  We  are  therefore  driven  to 
conclude  that  the  ethereal  particles  vibrate  in  a  direction 
transverse,  or  at  right  angles,  to  the  direction  in  which  the 
wave  is  moving.  How  such  vibrations  would  make  the 
wave  different  on  different  sides  will  be  readily  seen  from 
the  following  illustration. 

If  a  b  (Figure  92)  be  a  rope  fastened  at  a  and  held  by  the 

hand  at  b.  and  the  hand 

Fig.  92. 

be  moved  up  and  down, 
waves  will  run  along  the 
cord  in  the  direction  of 
its  length.  The  particles 
of  the  cord  will  vibrate  up  and  down,  or  transversely  to 
this  direction  of  the  waves.  The  cord  thus  vibrating  rep- 
resents a  ray  of  light  in  which  the  vibrations  are  trans- 
verse, and  it  will  be  seen  at  a  glance  that  such  a  ray  will 
be  different  at  the  right  and  the  left  from  what  it  is  above 
and  below,  or,  in  other  words,  that,  like  polarized  light,  it 
has  sides. 

If  the  hand  be  moved  to  and  fro  horizontally,  the  sides 
will  be  above  and  below  rather  than  at  the  right  and  the 
left,  as  at  first.  If  the  cord  in  the  first  case  be  taken  to 
represent  an  ordinary  ray,  it  will  in  the  second  case  repre- 
sent an  extraordinary  ray. 

If  the  hand  be  moved  rapidly  to  and  fro,  first  up  and 
down,  then  obliquely,  then  right  and  left,  and  so  on 
around,  the  particles  of  the  cord  will  be  made  to  vibrate 
in  these  different  directions  in  rapid  succession.  If  the 
particles  of  the  ether  are  vibrating  in  the  same  way,  it  is 
evident  that  the  ray  can  have  no  sides,  since  it  would  be 
alike  above  and  below,  to  the  right  and  to  the  left.  It  is 


LIGHT.  133 

possible,  then,  even  with  transverse  vibrations,  to  have  a 
ray  of  light  without  sides,  as  is  the  case  with  ordinary 
light. 

We  conclude,  then,  that  light  is  propagated  by  trans- 
verse vibrations ;  and  that  in  a  ray  of  ordinary  light  these 
vibrations  take  place  in  every  plane.  On  passing  through 
certain  crystals,  as  Iceland  spar,  these  vibrations  are  sifted 
and  arranged  in  two  sets ;  the  vibrations  in  one  set  being 
in  one  plane,  and  those  in  the  other  set  being  in  a  plane 
at  right  angles  to  this. 

One  of  these  sets  is  retarded  more  than  the  other  in 
passing  through  the  crystal,  and  is  therefore  bent  more 
from  its  course ;  and  this  is  generally  the  ordinary  ray. 

The  extraordinary  ray  also  passes  through  the  crystal 
more  readily  in  some  directions  than  in  others,  and  hence 
it  is  usually  refracted,  even  when  the  incident  ray  falls 
perpendicularly  upon  the  crystal ;  and  it  seldom  lies  in 
the  same  plane  with  the  incident  and  ordinarily  refracted 
rays. 

128.  Action  of  Tourmaline  on  Ordinary  Light.  —  If  a  ray 
of  ordinary  light  be  allowed  to  fall  upon  a  flat  plate  of 
tourmaline,  like  that  described  above,  and  the  transmitted 
light  be  allowed  to  fall  on  a  second  similar  plate,  it  will  be 
wholly  transmitted  when  the  plates  are  parallel,  and  wholly 
absorbed  when  they  are  at  right  angles ;  while  in  inter- 
mediate positions  it  will  be  partly  transmitted  and  partly 
absorbed.  If  the  light  which  has  been  transmitted  through 
the  first  plate  be  received  upon  a  plate  of  glass  at  an  angle 
of  incidence  of  56^°,  it  will  be  wholly  reflected,  in  a  certain 
position  of  the  glass,  and  wholly  transmitted  when  the 
glass  has  been  turned  round  through  90°.  The  ray  is 
reflected  and  transmitted  in  the  same  manner  as  the  ex- 
traordinary ray  obtained  by  refraction  in  a  crystal  of  Ice- 
land spar. 

The  tourmaline,  then,  not  only  impedes  one  set  of  vibra- 


134  LIGHT. 

tions  more  than  the  other,  but  wholly  absorbs  those  which 
are  parallel  to  its  optical  axis,  while  it  allows  those  at  right 
angles  to  this  axis  to  pass  readily. 

129.  Light  Polarized  by  Reflection  and  Refraction.  —  If  a 
ray  of  ordinary  light  A  C  ( Figure  93)  fall  upon  a  plate  of 

glass  PQ  at  an  angle  of 
incidence  of  56^°,  a  small 
part  CB  will  be  reflected, 
and  the  remainder  C  D 
transmitted.  On  exami- 
nation- the  reflected  por- 
tion will  be  found  to  be 
wholly  polarized  in  the 
plane  of  reflection  ;  and  the  refracted  portion  will  be  par- 
tially polarized  in  a  plane  at  right  angles  to  this ;  the 
refracted  beam  containing  just  as  much  polarized  light  as 
the  reflected  one.  At  any  other  angle  of  incidence  the 
reflected  portion  is  only  partially  polarized.  When  the 
reflected  ray  is  wholly  polarized,  as  above,  its  direction  is 
always  perpendicular  to  the  refracted  ray. 

Light  is  wholly  polarized  by  reflection  from  other  sub- 
stances, as  water,  diamond,  and  the  like ;  but  the  angle  at 
which  complete  polarization  takes  place,  or  the  polarizing 
angle,  as  it  is  called,  is  different  in  different  substances. 
For  water,  the  polarizing  angle  is  53°  n';  for  diamond, 
68°  6' ;  but  in  every  case  the  reflected  ray  is  perpendicular 
to  the  refracted  one. 

When  light  falls  upon  glass  at  the  polarizing  angle,  the 
reflected  portion  is,  as  we  have  seen,  wholly  polarized; 
but  the  reflected  portion  is  only  about  ^  that  of  the  trans- 
mitted, and  consequently  has  but  feeble  intensity.  If,  how- 
ever, several  plates  of  glass  are  laid  one  upon  another,  as 
in  Figure  94,  more  and  more  of  the  light  will  be  polarized 
on  reflection  from  each  surface.  In  this  way,  if  plates 
enough  are  used,  the  ray  will  be  divided  into  two  nearly 


LIGHT.  135 

equal  portions,  each  wholly  polarized  in  planes  at  right 
angles  to  each  other.  A  frame  containing  five  or  six 
squares  of  good  win-  Fig 

dow  glass,  laid  one  up- 
on another  and  backed 
with  a  piece  of  black 
velvet,  is  one  of  the 
cheapest  and  best  in- 
struments for  getting 
polarized  light 

130.  Polarizer    and 

Analyzer.  —  Any  instrument  used  to  polarize  light  is  called 
a  polarizer ;  and  any  instrument  used  to  examine  polarized 
light  is  called  an  analyzer.  Thus  a  tourmaline  plate,  when 
used  to  polarize  light,  is  a  polarizer ;  but  when  used  to 
examine  polarized  light,  it  is  an  analyzer. 

131.  Nicofs  Prism.  —  NicoFs  prism  is  one  of  the  most 
valuable  means  of  polarizing  light,  for  it  is  perfectly  color- 
less, polarizes  light  completely,  and,  like  tourmaline,  allows 
only  one  beam  to  pass.     It  is  made  from  a  rhomb  of  Ice- 
Fig.  95.  land  spar,  about  an  inch 

in  height,  and  a  third  of 
an  inch  in  breadth.  The 
rhomb  is  first  bisected  in 
the  plane  which  passes 
through  the  obtuse  angles,  as  shown  in  Figure  95.  The 
two  halves  are  then  joined  together  again  with  Canada 
balsam. 

The  principle  of  Nicol's  prism  is  this  :  the  refractive 
index  of  Canada  balsam  (1.549)  is  less  than  the  ordi- 
nary index  of  Iceland  spar  (1.654),  but  greater  than  its 
extraordinary  index  (1.483).  Hence,  when  a  luminous 
ray  S  C  (Figure  96)  enters  the  prism,  the  ordinary  ray 
undergoes  total  reflection  at  the  surface  of  the  Canada 
balsam  a  £,  and  takes  the  direction  C  d  O,  and  thus  is 


i36 


LIGHT. 


Fig.  96. 


carried  out  of  the  prism ;  while  the  extraordinary  ray  Ce 
emerges  alone.     This  prism  can,  like  tourmaline,  be  used 

either  as  a  polarizer  or  an 
analyzer.  It  is  better  than 
tourmaline,  since  the  latter 
is  always  colored. 

132.  Interference  of  Polar- 
ized Light.  —  Two  rays  are 
said  to  be  similarly  polar- 
ized when  they  are  polarized  in  the  same  plane,  and  op- 
positely polarized  when  polarized  in  planes  at  right  angles 
to  each  other.  If  now  in  polarized  light  the  particles  all 
vibrate  in  the  plane  of  polarization,  it  will  at  once  be  seen 
that  only  similarly  polarized  rays  can  interfere  so  as  to 
destroy  each  other ;  for  it  will  be  remembered  that,  where 
waves  interfere,  the  particles  are  compelled  to  remain  at 
rest  by  being  urged  by  equal  forces  to  move  in  opposite 
directions.  This  of  course  cannot  take  place  when  par- 
ticles are  moving  to  and  fro  in  planes  at  right  angles  to 
each  other,  but  only  when  they  are  moving  to  and  fro  in 
the  same  plane. 

Cut  two  parallel  slits  very  near  each  other  in  an  opaque 
screen,  place  it  before  a  brilliant  point  of  light,  examine  it 
with  a  magnifying  glass,  and  interference  fringes  will  be 
seen.  Cover  now  both  slits  with  exactly  similar  plates  of 
tourmaline.  When  the  plates  are  parallel,  the  rays  which 
they  transmit  are  similarly  polarized  ;  when  they  are  at 
right  angles  to  each  other,  the  transmitted  rays  are  oppo- 
sitely polarized.  In  the  first  case  the  fringes  are  distinctly 
seen,  but  they  wholly  disappear  in  the  second. 

We  thus  see  that  experiment  and  theory  agree  with 
respect  to  the  interference  of  polarized  light. 

133.  Circular  and  Elliptical  Polarization.  —  Although 
vibrations  cannot  destroy  each  other  unless  they  are  per- 
formed in  the  same  plane,  it  does  not  follow  that  they 


LIGHT.  137 

cannot  disturb  each  other  at  all.  When  a  boat  is  rowed 
against  a  stream  with  a  force  just  equal  to  that  of  the 
current,  it  remains  at  rest.  When,  however,  it  is  rowed 
across  the  stream,  it  does  not  remain  at  rest,  although  it 
does  not  take  the  same  course  it  would  were  there  no  cur- 
rent. In  this  case  the  boat  would  move  in  a  straight  line, 
and  in  a  direction  diagonal  to  that  of  the  current  and  that 
in  which  the  boat  is  rowed.  Again,  when  a  ball  is  thrown 
horizontally,  it  does  not  move  in  a  straight  line,  as  it  would 
were  no  other  force  acting  upon  it,  but  is  compelled  by 
gravity  to  move  in  a  curved  path.  So,  too,  when  two 
rays  of  light  whose  vibrations  are  performed  in  different 
planes  meet,  the  resulting  vibrations  are  sometimes  in  a 
direction  diagonal  to  those  of  the  components  ;  and  some- 
times, instead  of  moving  to  and  fro  in  straight  lines,  the 
particles  are  made  to  describe  curved  paths.  When  they 
are  made  to  move  in  circles,  the  light  is  said  to  be  cir- 
cularly polarized,  and  when  they  move  in  ellipses,  it  is 
said  to  be  elliptically  polarized. 

When  a  ray  of  polarized  light  is  reflected  from  a  pol- 
ished surface  in  a  different  plane  from  that  in  which  it  is 
polarized,  it  becomes  elliptically  polarized ;  when  it  is 
reflected  from  a  metallic  surface,  this  ellipticity  becomes 
very  considerable.  When  such  a  ray  is  totally  reflected, 
it  may  become  circularly  polarized. 

134.  Rotatory  Polarization. — When  a  ray  of  polarized 
light  is  transmitted  along  the  optical  axis  of  quartz  and  a 
few  other  crystals,  and  through  certain  liquids,  its  plane  of 
polarization  is  twisted  round  more  or  less,  according  to 
the  thickness  of  the  medium  traversed.  This  is  called 
rotatory  polarization.  Some  substances  turn  the  ray  round 
to  the  right,  and  some  to  the  left,  but  the  same  substance 
always  turns  it  in  the  same  direction.  The  amount  of 
twisting  of  the  ray  is  different  for  each  of  the  prismatic 
colors. 


138  LIGHT. 

Light  polarized  in  this  way  appears  to  the  unaided  eye 
like  ordinary  light.  When,  however,  it  is  analyzed  by 
Nicol's  prism  or  a  tourmaline  plate,  the  light  appears 
colored,  the  tint  varying  with  the  thickness  of  the  medium 
traversed  by  the  ray.  For  the  same  thickness  of  the  me- 
dium, the  tints  change  as  the  analyzer  is  turned  round 
the  ray.  When  the  plane  of  polarization  has  been  rotated 
to  the  right,  we  get  a  certain  succession  of  tints  on  turning 
the  analyzer  to  the  right.  When  the  plane  has  been 
rotated  to  the  left,  we  get  the  same  succession  of  tints  on 
turning  the  analyzer  to  the  left.  These  tints  therefore 
enable  us  to  detect  this  kind  of  polarized  light,  and  to 
determine  whether  the  plane  has  been  rotated  to  the  right 
or  to  the  left. 

A  solution  of  sugar  rotates  the  plane  of  polarization  to 
the  left,  and  the  amount  of  sugar  in  a  solution  can  be 
ascertained  by  passing  a  ray  of  polarized  light  through  it, 
and  noticing  the  tints  which  it  gives  upon  analysis.  An 
instrument  used  for  this  purpose  is  called  a  saccharometef 
(sugar-measurer. ) 

The  production  of  the  tints  when  this  kind  of  polarized 
light  is  analyzed  is  easily  explained.  Suppose  a  tourmaline 
plate  is  used  as  the' analyzer.  It  will  be  remembered  that 
the  amount  of  polarized  light  absorbed  by  such  a  plate 
varies  with  the  plane  of  polarization.  Now,  as  the  plane 
of  each  prismatic  color  is  rotated  a  different  amount,  it 
follows  that  the  colors  will  be  absorbed  in  different 
proportions  by  the  tourmaline,  and  the  transmitted  ray 
of  light  cannot  therefore  be  white,  but  must  be  of  the 
color  complementary  to  that  absorbed.  As  the  plate 
is  turned  round,  the  tints  will  change,  since  the  pro- 
portion in  which  the  different  colors  are  absorbed  will 
change. 

When  a  Nicol's  prism  is  used  as  an  analyzer,  the  differ- 
ent tints  are  due  to  the  fact  that  only  one  of  the  rays  is 


LIGHT.  139 

transmitted,  and  that  the  amount  of  light  which  passes  into 
the  ordinary  and  extraordinary  ray  differs  with  the  angle 
of  polarization  and  the  position  of  the  prism  with  reference 
to  the  ray. 

135.  Colors  exhibited  by  Crystalline  Plates  on  Exposure 
to  Polarized  Light.  —  If  a  crystalline  plate  cut  from  a  uni- 
axial  crystal  perpendicular  to  the  optical  axis  be  held  be- 
tween the  eye  and  a  source  of  polarized  light,  nothing  is 
seen  which  would  lead  to  the  suspicion  that  the  plate  is 
anything  more  than  an  ordinary  piece  of  glass.  If,  how- 
ever, the  light  which  has  passed  through  the  plate  be  ana- 
lyzed before  it  enters  the  eye,  a  series  of  brilliantly  colored 
rings  will  appear.  These  rings  change  their  color  and 
their  brilliancy  as  the  analyzer  is  turned  round.  When 
the  analyzer  is  in  one  position,  the  rings  are  crossed  by 
two  white  bars  at  right  angles  to  each  other  (Figure  97) ; 
and  when  the  analyzer  has  been  turned  through  90°, 
these  white  bars  are  replaced  by  black  ones  (Figure  98), 

Fig.  97.  Fig.  98. 


while  the  colors  of  the  rings  are  changed  to  their  com- 
plementary ones. 

When  the  plates  are  properly  cut  from  biaxial  crystals, 
two  sets  of  rings  and  bars  are  seen,  as  shown  in  Figures 
99,  100,  and  101. 

These  rings  are  due  to  the  interference  of  polarized 
rays.  Their  mode  of  formation,  and  the  reason  that 


140 


LIGHT. 


they  appear  only  when  the  analyzer  is  used,  will  be  evi- 
dent on  referring  to  Figures  102  and  103.     Every  ray  of 


Fig.  og. 


Fig.  100. 


Fig.  lox. 


polarized  light  diverging  from  P  is  separated,  on  passing 
through  the  crystalline  plate  C,  into  an  ordinary  and  an 


Fig.  102. 


Fig.  103. 


extraordinary  ray.  The  only  rays  which  would  come  to- 
gether so  that  they  could 
interfere,  as  seen  in  Fig- 
ure 102,  are  the  ordinary 
ray  of  one  set  and  the  ex 
traordinary  ray  of  the  next, 
as  o  e1  and  o'  e".  These 
rays  are  unequally  retard- 
ed in  passing  through  the  plate,  and  would  therefore  be  in  a 


LIGHT. 


141 


condition  to  interfere  were  they  not  oppositely  polarized. 
When,  however,  these  rays  fall  on  the  analyzer  A,  each  is 
again  divided  into  an  ordinary  and  an  extraordinary  ray. 
Of  these  rays  two  are  suppressed,  while  two,  polarized  in 
the  same  plane,  are  allowed  to  pass  on,  and  in  doing  so 
interfere  and  produce  the  colored  rings. 

136.  Other  Phenomena  of  Polarization. — Transparent 
substances,  like  glass,  when  their  particles  are  subjected  to 
unequal  strain,  have  the  same  effect  upon  polarized  light 
as  crystalline  plates.  If  a  ray  of  polarized  light  be  allowed 
to  pass  through  a  plate  of  well-annealed  glass,  and  then  be 
examined  with  the  analyzer,  no  colored  rings  appear. 
Rings,  however,  appear  as  soon  as  any  strain  is  brought  to 
bear  upon  the  glass  either  by  pressure  or  by  the  unequal 
heating  of  its  parts.  When  unannealed  glass  is  used,  the 
rings  are  very  brilliant,  and  have  different  forms  accord- 


Fig.  104. 


Fig.  105. 


Fig.  106. 


Fig.  107.  Fig.  108.  Fig.  109. 

ing  to  the  way  in  which  the  glass  is  cut,  as  shown  in 
Figures  104-109. 


142  LIGHT. 

Again,  place  a  piece  of  borax  glass  within  a  helix  of 
copper  wire,  and  allow  a  ray  of  polarized  light  to  pass 
through  it.  The  ray  is  unchanged;  but  as  soon  as  the 
electric  current  is  sent  through  the  helix,  the  plane  of 
polarization  is  twisted  round ;  showing  that  the  electric 
current  changes  the  condition  of  the  glass,  as  it  would 
change  that  of  iron  under  the  same  circumstances.  The 
effect  of  the  electric  current  upon  the  glass  is  however 
shown  in  nothing  else  than  its  action  upon  polarized 
light. 

In  polarized  light  we  have  a  most  delicate  means  of  ex- 
amining the  molecular  condition  of  a  transparent  body, 
since  it  reveals  the  slightest  change  in  this  condition,  and 
also  tells  us  whether  or  not  the  substance  is  crystalline  in 
structure. 

137.  The  Tourmaline  Pincette.  —  The  colors  exhibited  by 
polarized  light  are  exceedingly  beautiful.  The  simplest 
and  most  convenient  apparatus  for  showing  these  colors  is 
given  in  Figure  in,  and  is  called  the  tourmaline  pincette. 
It  consists  of  two  tourmaline  plates  cut  parallel  to  the  axis, 
mounted  as  shown  in  the  figure.  The  plates  are  so  ar- 
ranged that  they  can  be  turned  round  and  inclined  to  each 

Fig.  no.  Fig.  in. 


M 


other  at  any  angle.  The  plate  to  be  examined  is  fastened 
to  the  centre  of  a  cork  disc  M  (Figure  no),  and  then 
placed  between  the  tourmalines.  The  pincette  is  then 
held  before  the  eye  in  diffused  daylight.  The  tourmaline 
farthest  from  the  eye  acts  as  a  polarizer,  and  the  other  as 
an  analyzer. 


LIGHT.  143 


SUMMARY. 

When  a  ray  of  light  passes  through  a  crystal  of  Iceland 
spar  it  is  usually  doubly  refracted,  one  of  the  refracted  rays 
being  called  the  ordinary,  and  the  other  the  extraordinary 
ray. 

When  a  doubly  refracting  crystal  converts  both  portions 
into  extraordinary  rays,  it  is  called  a  biaxial  crystal.  (124.) 

The  ordinary  and  extraordinary  rays  can  be  separated 
by  a  doubly  refracting  prism.  (125.) 

Both  the  doubly  refracted  rays  have  acquired  sides,  and 
are  said  to  be  polarized.  They  are  polarized  in  planes 
at  right  angles  to  each  other.  (126.) 

Polarization  shows  that  light  is  propagated  by  transverse 
vibrations  ;  and  that  in  ordinary  light  these  vibrations  are 
executed  in  every  plane,  while  in  polarized  light  they  are 
executed  in  only  one  plane.  (127.) 

Tourmaline  absorbs  one  of  the  polarized  rays.     (128.) 

Light  may  be  polarized  by  reflection,  and  by  single  re- 
fraction. (129.) 

The  polariscope  consists  of  a  polarizer  and  an  analyzer. 
(130.) 

Nicol's  prism  is  constructed  so  as  to  shut  out  one  of  the 
polarized  rays.  (131.) 

Polarized  rays  can  interfere  so  as  to  destroy  each  other 
only  when  they  are  polarized  in  the  same  plane  ;  but  they 
may  interfere  so  as  to  produce  circular,  elliptical,  and 
rotatory  polarization  when  they  are  polarized  in  different 
planes.  (132-134.) 

When  crystalline  plates  are  examined  in  polarized  light 
by  means  of  an  analyzer,  they  exhibit  interference  rays. 


Polarized  light  affords  an  excellent  means  of  examining 
the  molecular  condition  of  bodies.     (136.) 


144  LIGHT. 


THE  RAINBOW. 

138.  The  Appearance  of  the  Rainbow.  —  The  rainbow,  in 
its  most  perfect  form,  consists  of  two  colored  arches  pro- 
jected upon  falling   rain  upon  which   the  sun  is  shining 
from  the  opposite  quarter  of  the  heavens.     The  lower  or 
inner  arch  is  called  the  primary  bow ;  the  upper  or  outer, 
the  secondary  bow.     Each  contains  all  the  colors  of  the 
spectrum,  but  the  order  of  the  colors  in  one  is  the  reverse 
of  that  in  the  other.     Red  is  outermost  in  the  primary 
bow,  and  innermost  in  the  secondary.     The  primary  bow 
is  the  narrower  and  brighter  of  the  two,  and  when  it  is  of 
unusual  brightness  narrow  red  arches  are  seen  just  within 
it,  called  supernumerary  bows.     These  are  sometimes  three 
or  four  in  number,  but  they  can  be  traced  only  a  short 
distance.     The  common  centre  of  the  bows  is  in  a  line 
drawn  from  the  sun  through  the  eye  of  the  observer. 

139.  The  Cause  of  the  Rainbow. — The  rainbow  is  pro- 
duced by  the  refraction  and  reflection  of  the  sunlight  with- 
in the  rain-drops.      Its  colors   are  due   partially  to   the 
dispersion,  and  partially  to  the  interference  of  the  light 


thus  refracted  and  reflected.      Let  the  circle  in  Figure  112 


LIGHT.  145 

be  a  drop  of  rain.  A  ray  of  sunlight  S  A  which  passes 
through  the  centre  of  the  drop  will  not  be  refracted,  since 
it  meets  the  surface  of  the  drop  perpendicularly ;  and  the 
portion  of  it  reflected  at  n  will  be  thrown  directly  back. 
As  we  pass  from  A  to  a  the  rays  become  refracted  more 
and  more,  since  they  meet  the  surface  of  the  drop  more 
and  more  obliquely,  and,  on  being  reflected  from  the  inner 
surface  of  the  drop,  emerge  in  directions  differing  more 
and  more  from  A  S.  The  ray  s  a  takes  the  direction 
abed;  the  ray  s  B,  the  direction  Bgep.  As  we  pass 
beyond  B  the  rays  are  refracted  so  much  that  they  begin 
to  fall  below  g,  and  continue  to  fall  farther  and  farther 
below  it  until  we  come  to  C,  where  the  rays  begin  to  pass 
by  the  drop.  Hence  all  the  light  which  falls  upon  the 
drop  between  A  and  C  is  refracted  upon  the  inner  surface 
between  g  and  n.  The  light  which  falls  upon  the  drop  for 
a  considerable  distance  each  side  of  B  is  refracted  very 
nearly  to  g,  and,  on  being  reflected,  emerges  from  the  drop 
very  nearly  in  the  direction  ep;  while  the  rays  falling  upon 
the  drop  farther  from  B  are,  on  emerging  from  the  drop, 
scattered  over  the  space  between  e  and  A.  Hence  the 
light  which  emerges  from  the  drop  after  refraction  and  re- 
flection is  much  more  intense  in  the  direction  e p  than 
elsewhere ;  and  it  is  only  here  that  it  is  intense  enough  to 
affect  the  eye  at  any  distance. 

But  the  light  which  falls  upon  the  drop  a  little  below 
B  has  to  traverse  a  slightly  different  distance  in  passing 
through  the  drop  than  that  which  falls  upon  it  a  little 
above  B.  Hence  these  portions  of  light  are  unequally  re- 
tarded in  passing  through  the  drop,  and  therefore  emerge 
from  it  with  their  waves  in  somewhat  different  phases,  so 
that  they  are  in  a  condition  to  interfere.  Since  the  differ- 
ent-colored rays  are  differently  refracted  in  passing  through 
the  drop,  the  direction  ep  in  which  the  light  emerges  with 
the  greatest  intensity  is  not  the  same  for  the  different 
7  J 


146 


LIGHT. 


colors.  For  red  light  the  direction  ep  differs  from  that  of 
A  S,  or  of  the  sun's  rays,  by  an  angle  of  about  42°  ;  while 
for  violet  light  these  directions  differ  by  an  angle  of  about 
40°.  For  the  other  colors  the  difference  of  direction  is 
intermediate  between  these  two. 

As  the  emerging  rays  of  each  of  the  colors  are  in  a  con- 
dition to  interfere,  they  will  of  course  give  rise  to  colored 
bands  separated  by  dark  spaces.  Let  us  consider  the  first 
bright  band  of  each  color.  Suppose  a  person  is  looking 
at  rain-drops  illumined  by  the  sun  when  near  the  horizon. 
Wherever  he  can  direct  his  eye  so  that  a  line  drawn  from 
it  to  a  rain-drop  shall  make  an  angle  of  42°  with  a  line 
drawn  from  the  same  drop  to  the  sun,  as  at  r  in  Figure  1 13, 

Fig.  113. 


he  will  see  a  band  of  red  light ;  and  since  the  drops  are 
spread  out  over  all  the  space  before  him,  and  since  the 
sun's  rays  are  all  parallel,  this  band  will  evidently  be 


LIGHT.  147 

continuous,  and  will  have  the  form  of  an  arc  of  a  circle. 
The  centre  of  this  arc  will  lie  in  a  line  drawn  from  the  sun 
through  the  eye  of  the  observer,  and  its  radius  will  be  42°. 
Whenever  he  can  see  a  drop,  as  at  v,  such  that  a  line 
drawn  from  his  eye  to  it  shall  make  an  angle  of  40°  with 
a  line  drawn  from  the  drop  to  the  sun,  he  will  see  a  band 
of  violet  light.  This  band  also  will  have  the  form  of 
an  arc  of  a  circle  whose  radius  is  40°,  and  whose  cen- 
tre is  the  same  as  that  of  the  red  arc.  Between  these 
two  bands  will  be  seen  the  bands  of  the  other  prismatic 
colors. 

The  first  band  of  each  of  the  other  prismatic  colors  is 
situated  between  the  first  and  second  bright  bands  of  the 
red  light ;  while  the  second  band  of  each  of  these  colors 
falls  outside  of  the  first  violet  band.  This  is  the  reason 
of  the  purity  of  the  colors  of  the  rainbow.  The  second 
band  of  each  of  the  colors  is  much  feebler  than  the  first, 
seldom  bright  enough  to  be  visible.  When  bright  enough 
to  be  visible,  they  form  the  supernumerary  bows/^. 

The  outer  bow  is  caused  by  the  rays  which  meet  the  eye 
after  being  twice  reflected  within  the  rain-drop,  as  seen  at 
/  and  if.  It  is  owing  to  this  double  reflection  that  the 
colors  are  feebler  than,  and  in  the  reverse  order  of  those 
in  the  primary  bow,  where  the  light  is  reflected  but  once. 

SUMMARY. 

The  rainbow  is  seen  opposite  the  sun. 

It  contains  all  the  colors  of  the  spectrum,  the  red  being 
outermost  in  the  primary  bow  and  innermost  in  the  sec- 
ondary. (138.) 

The  rainbow  is  produced  by  the  refraction  and  reflection 
of  light  within  the  rain-drop. 

The  colors  of  the  bow  are  due  partly  to  dispersion,  and 
partly  to  interference.  (139.) 


i48 


LIGHT. 


OPTICAL   INSTRUMENTS. 
LENSES. 

140.  Forms  of  Lenses.  —  Lenses  are  pieces  of  glass,  or 
other  transparent  substance,  bounded  on  one  or  both  sides 
by  a  curved  surface.  The  forms  of  lenses  used  in  optical 
instruments  are  shown  in  Figure  114.  A  is  bounded  by 

Fig.  114. 
ABC  D  E          F 


two  spherical  surfaces,  and  is  called  a  double-convex  lens. 
B  has  a  spherical  surface  on  one  side,  and  a  plane  surface 
on  the  other,  and  is  called  a  plano-convex  lens.  C  has  a 
convex  surface  on  one  side,  and  a  slightly  concave  surface 
on  the  other,  and  is  called  a  meniscus,  from  a  Greek  word 
meaning  a  crescent.  D  has  two  concave  surfaces,  and  is 
called  a  double-concave  lens.  E  has  a  concave  and  a  plane 
surface,  and  is  called  a  plano-concave  lens.  F  has  a  con- 
cave surface  on  one  side  and  a  slightly  convex  surface  on 
the  other,  and  is  called  a  concavo-convex  lens. 

Allow  a  beam  of  sunlight  to  fall  upon  a  double-convex 
lens  in  a  darkened  room.  On  leaving  the  lens,  the  rays 
will  converge  to  a  point,  called  the  focus  (the  Latin  word 
for  fireplace],  since  the  heat  as  well  as  the  light  is  concen- 
trated there.  This  action  of  the  lens  upon  the  light  will 
be  understood  from  Figure  115.  It  will  be  seen  that  the 
section  of  the  lens  is  like  that  of  two  prisms  placed  back 
to  back ;  and  it  will  be  remembered  that  a  ray  of  light,  in 
passing  through  a  prism,  is  bent  twice  in  the  same  direc- 


LIGHT.  149 

tion.      The  rays  falling  upon  the  upper  part  of  the  lens 
will  be  bent  downward,  and  those  falling  on  the  lower 


115. 


part  will  be  bent  upward,  and  they  will  all  meet  at  F. 

If  a  beam  of  sunlight  be  allowed  to  fall  on  a  plano-con- 
vex lens  or  a  meniscus,  the  rays  will  also  be  converged  to 
a  focus. 

If,  however,  we  use  any  one  of  the  concave  lenses,  it  will 
be  found  that  the  rays  of  light, 
instead  of  converging,  are  made  Flg-  II6' 

to  diverge,  on  leaving  the  lens. 
The  reason  of  this  divergence 
will  be  evident  from  Figure  1 1 6. 

Since  the  convex  lenses  all 
cause  parallel  rays  to  converge, 
they  are  called  convcrging\&bS£& ; 
while  the  concave  lenses  are  called  diverging  lenses,  since 
they  cause  parallel  rays  to  diverge. 

141.  Images  formed  by  Lenses.  —  Place  a  lighted  candle 
before  a  double-convex  lens  in  a  darkened  room,  and  a 
screen  behind  it.  It  will  be  found  that,  at  a  certain  dis- 
tance from  the  lens,  a  distinct  inverted  image  of  the  candle 
will  be  formed  upon  the  screen.  Move  the  candle  nearer 
the  lens,  and  the  image  will  become  blurred,  but  will  be- 
come distinct  again  on  moving  the  screen  farther  from  the 
lens.  If  the  candle  be  moved  away  from  the  lens,  the  image 
becomes  blurred ;  but  it  becomes  distinct  again  when  the 


150  LIGHT. 

screen  is  brought  nearer  the  lens.     The  nearer  the  candle 
is  to  the  lens,  the  larger  the  image  formed. 

If  now  the  lens  be  taken  away,  and  one  of  greater  con- 
vexity be  used,  it  will  be  found  that  the  candle  must  be 
brought  nearer  the  lens  in  order  that  its  image  may  be 
formed  upon  the  screen,  and  the  image  becomes  larger. 
The  more  convex  the  lens  used,  the  nearer  the  candle 
must  be  brought  to  it,  and  the  larger  the  image.  If,  on 
the  other  hand,  a  less  convex  lens  be  used,  the  candle 
must  be  put  fjarther  off,  and  the  image  becomes  smaller. 

Instead  of  using  a  more  convex  lens,  we  may  add  a 
second  convex  lens,  with  the  same  effect. 

Let  us  suppose  that  the  lens  is  made  of  some  elastic 
substance,  so  that  we  may  change  its  convexity  by  pulling 
out  or  pushing  in  its  sides  ;  and  that  the  lens  is  first  made 
very  flat,  so  that  an  image  is  formed  upon  the  screen  when 
the  candle  is  at  a  great  distance.  If  we  move  the  candle 
nearer,  the  lens  must  be  made  more  and  more  convex,  in 
order  to  keep  the  image  on  the  screen  distinct,  and  the 
image  at  the  same  time  will  grow  larger  and  larger. 

When  the  candle  and  the  screen  are  both  at  the  same 
distance  from  the  lens,  the  image  will  be  of  the  same  size 
as  the  candle ;  when  the  candle  is  farther  from  the  lens 
than  the  screen  is,  the  image  will  be  smaller  than  the 
candle ;  and  when  the  candle  is  nearer  the  lens  than  the 
screen  is,  the  image  will  be  larger  than  the  candle. 

Why  the  image  is  thus  formed  on  the  screen  will  be  evi- 
dent from  Figure  117.  All  the  light  which  radiates  from 
the  point  A  of  the  candle  is  refracted,  in  passing  through 
the  lens,  and  concentrated  at  a;  and  all  radiating  from  B 
is  concentrated  at  b,  and  all  radiating  from  points  between 
A  B  will  be  concentrated  at  corresponding  points  between 
a  and  b.  Hence  the  space  between  a  and  b  must  have  the 
same  light  and  shade  as  the  flame  itself,  and  must  there 
fore  appear  exactly  like  it. 


LIGHT.  151 

It  will  be  seen  that  the  image  lies  between  the  lines, 
A  a  B  l>,  drawn  from  the  extremities  of  the  object  through 

Fig.  117. 


the  centre  of  the  lens.  It  follows  from  this  that  the  image 
and  the  object  must  be  of  the  same  size  when  they  are  at 
the  same  distance  from  the  lens,  and  that  the  one  which  is 
nearer  the  lens  must  be  the  smaller. 

The  reason  why  the  image  recedes  from  the  lens  as  the 
object  approaches  is  also  evident.  As  the  object  ap- 
proaches, the  rays  which  fall  upon  the  lens  become  more 
and  more  divergent,  and  of  course  will  not  meet  so  soon 
on  the  other  side  of  the  lens. 

The  place  where  the  image  is  formed  is  called  the  focus 
of  the  lens  (140). 

The  focus  of  a  lens,  then,  changes  with  the  divergence  of 
the  rays  which  fall  upon  it.  The  point  where  parallel  rays 
are  made  to  meet  is  called  the  principal  focus. 

If  an  object  were  placed  in  the  principal  focus,  the  rays 
diverging  from  it  would  become  parallel,  on  emerging  from 
the  lens.  If  the  object  were  placed  nearer  the  lens 
than  the  principal  focus  is,  the  rays  would  be  still  diver- 
gent on  leaving  the  lens,  though  less  so  than  on  enter- 
ing it. 


152  LIGHT. 


SUMMARY. 

There  are  two  classes  of  lenses.  One  class  causes 
parallel  rays  to  converge,  and  the  other  causes  them  to 
diverge.  (140.) 

When  objects  are  placed  in  front  of  a  converging  lens, 
images  of  them  are  formed  at  its  focus  behind  it. 

The  magnitude  of  the  image  increases  with  its  distance 
from  the  lens,  and  also  with  the  convexity  of  the  lens. 

The  image  is  of  the  same  size  as  the  object  when  it  is 
the  same  distance  from  the  lens,  smaller  when  it  is  nearer 
the  lens,  and  larger  when  it  is  farther  from  it.  (141.) 

THE  EYE. 

142.  The  Camera  Obscura.  —  If  a  converging  lens  be 
placed  before  an  opening  in  the  shutter  of  a  darkened 
room,  a  small  and  beautiful  picture  of  the  landscape  will 
be  seen  upon  a  screen  placed  a  short  distance  behind  the 
lens.  In  this  picture  every  motion  of  the  branches  and 
leaves  of  the  trees  and  all  other  objects  will  be  exactly 
delineated.  An  arrangement  of  this  kind  by  which  im- 
ages of  external  objects  are  formed  upon  a  screen  in  a 
darkened  room  is  called  a  camera  obscura. 

Figure  118  represents  the  camera  used  by  photographers. 
C  is  a  dark  chamber ;  E  is  the  screen  of  ground  glass 
upon  which  the  image  is  received ;  A  is  a  tube  containing 
the  combination  of  lenses  used  to  form  the  image.  This 
camera  can  be  adjusted  to  objects  at  different  distances  by 
changing  the  position  of  the  screen,  or  of  the  lenses  (which 
may  be  moved  by  the  screw  Z>),  or  both. 

In  the  ordinary  camera  the  image  is  smaller  than  the 
object,  since  it  is  nearer  the  lens. 

Any  transparent  substance  with  convex  surfaces,  placed 


153 


in  a  medium  less  refractive  than  itself,  causes  the  rays  of 
light  traversing  this  medium  to  converge  to  a  focus.  If  a 
watch-glass  be  fitted  into  the  side  of  a  box,  and  the  box  be 
filled  with  water,  a  candle  may  be  placed  at  such  a  dis- 
tance in  front  of  the  watch-glass  that  an  image  of  its  flame 
shall  be  formed  on  the  opposite  wall  of  the  box.  If  now 
a  convex  lens  of  glass  be  introduced  into  the  water  in  the 
path  of  the  rays,  it  will  cause  them  to  come  to  a  focus 
sooner,  because  glass  refracts  light  more  strongly  than 
water  does.  An  arrangement  like  the  above  might  be 
called  a  water  camera. 

143.  The  Eye  a  Water  Camera. — The  eyeball  is  com- 
posed, in  the  first  place,  of  a  tough,  firm,  spherical  case, 
Scl  (Figure  119).  The  greater  part  of  this  case  is  white 
and  opaque,  and  is  called  the  sclerotic  coat,  or  the  white  of 
the  eye.  In  front  this  case  becomes  transparent,  and  is 
called  the  cornea,  Cn.  The  cornea  is  more  convex  than 
the  sclerotic.  This  case  of  the  eye  is  kept  in  shape  by 
being  filled  with  fluids  called  the  humors.  One  of  these, 
the  aqueous  humor,  Aq,  fills  the  corneal  chamber ;  and  the 
other,  the  vitreous  humor,  £?,  the  sclerotic  chamber.  The 
two  humors  are  kept  separate  by  the  double-convex  crystal- 

7* 


154  LIGHT. 

line  lens,  Cry,  which  is  denser,  and  capable  of  refracting 
light  more  strongly,  than  either  humor.  The  crystalline 
lens  is  highly  elastic,  more  convex  behind  than  in  front, 


M.I. 


and  is  kept  in  place  by  a  delicate  but  very  strong  and 
elastic  ligament  which  extends  from  the  edge  of  the  lens  to 
what  are  called  the  ciliary  processes  of  the  choroid  coat. 
This  choroid  coat,  Ch,  is  of  a  dark  color  and  highly  vascu- 
lar (that  is,  full  of  vessels),  and  it  lines  the  whole  inner 
chamber  of  the  eye.  When  it  reaches  the  front  part  of  the 
chamber,  its  inner  surface  becomes  raised  into  longitudinal 
ridges  with  rounded  ends.  These  ridges  are  the  ciliary 
processes,  C.p. 

The  iris,  Ir,  is  a  curtain  with  a  round  hole  in  the  middle 
called  the  pupil.  The  iris  has  two  sets  of  muscular  fibres  ; 
one  circular  and  the  other  radiating.  By  the  action  of 
these  the  pupil  is  enlarged  or  contracted.  It  is  the  iris 
which  gives  the  color  to  the  eye  ;  and  hence  its  name. 

The  optic  nerve,  Op,  enters  the  back  of  the  eye  a  little 


LIGHT.  15 

way  from  the  centre  towards  the  nose.  It  then  spreadv 
out  over  the  choroid  coat,  forming  the  retina,  Rt. 

The  eyeball  is  thus  seen  to  be  a  water  camera.  The 
cornea  answers  to  the  watch-glass ;  the  sclerotic,  to  the 
box ;  the  humors,  to  the  water ;  and  the  crystalline  lens, 
to  the  glass  lens. 

In  an  ordinary  camera  it  is  found  desirable  to  have 
what  is  called  a  diaphragm,  to  moderate  the  light,  and  to 
cut  off  all  the  rays  except  those  which  fall  on  the  central 
part  of  the  lens.  In  the  eye  the  iris  acts  as  a  diaphragm, 
and  has  the  advantage  of  being  self-regulating.  It  dilates 
the  pupil  and  admits  more  light  when  the  illumination  is 
too  weak  ;  it  contracts  the  pupil  and  cuts  off  a  part  of  the 
light  when  there  is  too  much  of  it. 

144.  The  Adjustment  of  the  Eye.  — That  the  eye  must 
adjust  itself  in  order  to  see  distinctly  at  different  distances 
is  shown  by  the  following  simple  experiment.  Stick  two 
stout  needles  into  a  piece  of  wood,  so  that  one  of  them,  a, 
shall  be  about  six  inches  from  the  eye,  and  the  other,  b, 
.about  twelve,  very  nearly  in  the  same  direction.  If  now 
you  look  at  the  needle  b,  you  will  see  it  distinctly  and  with- 
out the  least  sense  of  effort ;  but  the  image  of  a  will  be 
blurred.  Try  now  to  make  this  blurred  image  of  a  distinct, 
and  you  find  that  you  can  do  it,  but  not  without  effort.  In 
proportion  as  a  becomes  distinct,  b  becomes  blurred,  and 
no  effort  will  enable  you  to  see  both  distinctly  at  the  same 
time. 

Very  many  explanations  have  been  given  of  this  remark- 
able power  of  adjustment  possessed  by  the  eye.  It  is  only 
within  a  few  years  that  it  has  come  to  be  clearly  under- 
stood. When  a  lighted  taper  is  held  near  and  a  little  to 
one  side  of  a  person's  eye,  any  one  on  looking  into  the 
eye  from  the  proper  position  will  see  three  images  of  the 
flame ;  one  reflected  from  the  cornea,  one  from  the  front 
surface  of  the  crystalline  lens,  and  one  from  its  rear  sur- 


'56 


LIGHT. 


face.  Suppose  now  the  person's  eye  be  steadily  fixed  on  a 
distant  object,  and  then  adjusted  to  a  nearer  one  in  the 
same  direction.  The  position  of  the  eyeball  of  course  re- 
mains the  same.  It  is  also  found  that  the  images  reflected 
from  the  cornea  and  from  the  rear  surface  of  the  lens  re- 
main unchanged;  while  the  image  reflected  from  the  front 
surface  of  the  lens  changes  its  position  and  size  in  such  a 
way  as  to  show  that  this  surface  has  been  brought  forward 
and  at  the  same  time  made  more  convex.  The  eye  then 

adjusts  itself  to  dif- 
ferent distances  by 
altering  the  convex- 
ity of  the  crystalline 
lens.  This  change 
in  the  form  of  the 
lens  is  shown  in 
Figure  120.  The 
half  A  shows  the  form  of  the  lens  when  the  eye  is  ad- 


Fig.  120. 


justed  for  distant  objects  ;  and  the 
half  B,  when  it  is  adjusted  for  near 
objects. 

145.  The  Structure  of  the  Retina.  — 
Figure  121  represents  a  portion  of 
the  retina  highly  magnified,  since 
the  whole  thickness  of  this  membrane 
does  not  exceed  the  ff\y  of  an  inch. 
The  inner  side  a,  which  is  in  contact 
with  the  vitreous  humor,  is  lined  with 
what  is  called  the  limiting  membrane. 
Externally  and  next  to  the  choroid 
coat  it  consists  of  a  great  number  of 
minute  rod-like  and  conical  bodies,  <?, 
arranged  side  by  side.  This  is  the 
layer  of  rods  and  cones,  and  occupies 
a  quarter  of  the  whole  thickness  of  the  retina. 


Fig.  121. 


From  the 


LIGHT.  157 

inner  ends  of  the  rods  and  cones  very  delicate  radial  fibres 
spread  out  to  the  limiting  membrane,  d  and  c  are  layers 
of  granules.  The  fibres  of  the  optic  nerve  are  all  spread 
out  between  b  and  a.  At  the  entrance  of  the  optic  nerve, 
the  nerve  fibres  predominate,  and  the  rods  and  cones  are 
wanting.  Exactly  at  the  centre  of  the  back  of  the  eye 
there  is  a  slight  circular  depression  of  a  yellowish  hue, 
called  the  macula  lutea,  or  yellow  spot.  In  this  spot  the 
cones  are  abundant  without  the  rods  and  nerve  fibres. 

146.  The  Action  of  Light  on  the  Optic  Nerve.  —  The  dis- 
tribution of  the  nerve  fibres  over  the  front  surface  of  the 
retina  would  seem  to  indicate  that  they  are  directly  acted 
upon  by  the  light ;  but  this  is  not  the  case.  The  fibres  of 
the  optic  nerve  are  in  themselves  as  blind  as  any  other 
part  of  the  body.  To  prove  this  we  have  only  to  close  the 
left  eye  and  with  the  right  look  steadily  at  the  cross  on  this 
page,  holding  the  book  ten  or  twelve  inches  from  the  eye. 


The  black  dot  will  be  seen  quite  plainly  as  well  as  the 
cross.  Now  move  the  book  slowly  towards  the  eye,  which 
should  be  kept  fixed  on  the  cross.  At  a  certain  distance 
the  dot  will  suddenly  disappear ;  but  on  bringing  the  book 
still  nearer  it  will  come  into  view  again.  Now  it  is  found 
upon  examination  that  when  the  dot  disappears  its  image 
falls  exactly  upon  the  point  where  the  optic  nerve  enters 
the  eye,  and  where  there  are  no  rods  and  cones,  but 
merely  nerve  fibres.  Again,  the  yellow  spot  is  the  most 
sensitive  part  of  the  retina,  though  it  contains  no  nerve 
fibres. 

It  would  appear,  then,  that  the  fibres  of  the  optic  nerve 
are  not  directly  affected  by  the  vibrations  of  the  ether,  but 
only  through  the  rods  and  cones.  This  view  is  confirmed 
by  the  following  experiment.  Go  into  a  dark  room  with  a 


158  LIGHT. 

candle  which  has  a  small  bright  flame,  and,  looking  towards 
the  dark  wall,  move  the  light  up  and  down  close  to  the 
outer  side  of  one  eye,  so  that  the  light  may  fall  very  ob- 
liquely upon  the  retina,  and  you  will  see  one  of  what  are 
called  Pur kinje^s  figures.  This  is  a  vision  of  a  series  of 
diverging  branched  red  lines  on  a  dark  field,  with  a  sort 
of  cup-shaped  disc  between  two  of  them.  The  red  lines 
are  the  blood-vessels  of  the  retina,  and  the  disc  is  the 
yellow  spot.  As  the  candle  is  moved  up  and  down,  the  red 
lines  shift  their  position,  as  shadows  do  when  the  light 
which  casts  them  changes  its  place.  Now  as  the  light 
falls  on  the  inner  face  of  the  retina,  and  the  images  shift 
their  position  as  it  moves,  whatever  perceives  these  images 
must  lie  on  the  other  or  outer  side  of  the  vessels  which 
gave  rise  to  the  images.  But  the  fibres  of  the  optic  nerve 
lie  in  front  of  the  retina  among  these  vessels ;  and  the  only 
parts  of  the  retina  which  lie  behind  the  vessels  are  the 
granular  layers  and  the  rods  and  cones. 

Thus  it  would  appear  that  these  remarkable  bodies,  set 
upon  the  inner  surface  of  the  retina  with  their  ends  turned 
towards  the  light,  are  like  so  many  finger-points,  endowed 
with  a  touch  delicate  enough  to  feel  che  luminous  vibra- 
tions and  convert  them  into  impulses  which  can  excite  the 
optic  nerve ;  just  as  the  otoliths  and  the  fibres  of  Corti 
in  the  ear  catch  and  convert  the  vibrations  of  the  fluids 
of  the  ear  into  impulses  which  can  excite  the  auditory 
nerve. 

147.  The  Sensation  of  Light  may  be  excited  by  Other 
Causes.  —  The  sensation  of  light  may  be  excited  by  any- 
thing which  can  excite  the  optic  nerve.  Thus  an  electric 
shock  sent  through  the  eye  gives  rise  to  an  apparent  flash 
of  light.  If  a  small  piece  of  zinc  be  held  in  the  mouth, 
and  one  end  of  a  silver  pencil-case  be  held  in  the,  corner 
of  the  eye,  a  flash  is  seen  when  the  silver  and  the  zinc 
are  brought  in  contact.  If  the  finger  be  pressed  on  one 


LIGHT.  159 

side  of  the  eyeball,  a  luminous  image  is  seen.  In  the 
same  way  a  blow  on  the  head  sometimes  makes  one  "  see 
stars." 

148.  The  Duration  of  the  Impression  on  the  Retina.  — 
The  impression  made  by  light  on  the  retina  does  not  cease 
the  instant  the  light  is  removed,  but  lasts  about  the  eighth 
of  a  second.     If  luminous  impressions  are  separated  by  a 
less  interval,  they  appear  continuous.     Thus,  if  a  stick  with 
a  spark  of  fire  at  the  end  be  whirled  round  rapidly,  it  gives 
the  impression  of  a  circle  of  light.     The  spokes  of  a  car- 
riage wheel  in  rapid  motion  cannot  be  distinguished. 

The  optical  toy  called  the  thaumatrope  illustrates  the 
same  principle.  It  consists  (Figure  122)  of  a  cylindrical 
paper  box  made  to  rotate  on  an  upright  f.  JM 

axis.  Near  the  top  of  the  box  is  a  row 
of  upright  slits.  The  successive  posi- 
tions which  a  moving  body  assumes  are 
represented  in  order  upon  a  strip  of 
paper ;  and  this  paper  is  put  within  the 
box,  which  is  then  whirled  round  rap- 
idly. If  we  look  at  the  figures  through 
the  slits,  the  successive  positions  come  before  the  eye  one 
after  another,  and  the  impression  of  each  lasts  till  the  next 
arrives,  so  that  they  all  blend  into  one,  and  the  object 
appears  to  be  really  going  through  the  evolutions  rep- 
resented. 

149.  Irradiation. — When  a  white  or  very  bright  object 
is  seen  against  a  black  ground  it  appears  larger  than  it 
really  is ;  while  a  black  object  on  a  white  ground  appears 
smaller  than  it  really  is.     The  two  circles  given  in  Figure 
123  illustrate  this.     The  black  one  and  the  white  one  have 
just  the  same  diameter. 

This  effect  is  called  irradiation.  It  arises  from  the  fact 
that  the  impression  produced  by  a  bright  object  on  the 
retina  extends  beyond  the  outline  of  the  image.  It  bears 


l6o  LIGHT. 

the  same  relation  to  the  space  occupied  by  the  image  as 
the  duration  of  the  impression  does  to  the  duration  of  the 
image. 

We  have  one  of  the  most  marked  cases  of  irradiation  in 

Fig.  123. 


the  moon  when  a  few  days  old.  The  new  moon  seems 
much  larger  than  the  old  one  which  it  is  said  to  "  hold  in 
its  arms.". 

150.  The  Sensibility  of  the  Retina  is  easily  exhausted.  — 
When  we  look  at  a  bright  light,  and  then  turn  the  eye  to- 
wards a  moderately  lighted  surface,  a  dark  spot  is  seen ; 
showing  that  the  part  of  the  retina  on  which  the  bright 
light  fell  has  lost  for  the  moment  its  sensibility,  or  become 
blind.  If  the  bright  object  be  of  one  color,  the  part  of  the 
retina  on  which  its  image  falls  becomes  insensible  to  rays 
of  that  color,  but  not  to  those  of  other  colors.  This  ex- 
plains the  appearance  of  what  are  called  complementary 
colors.  For  example,  if  a  red  wafer  be  stuck  upon  a 
sheet  of  white  paper,  and  viewed  steadily  for  some  time 
with  one  eye,  and  then  the  eye  be  turned  to  another  part 
of  the  paper,  a  greenish  spot  will  appear  of  the  size  and 
shape  of  the  wafer.  The  red  image  has  made  the  retina 
blind  to  red  light,  but  it  has  left  it  sensitive  to  the  remain- 
ing colors  which  make  up  white  light ;  and  when  red  is 
taken  from  white  light  the  combination  of  the  other  colors 
gives  a  greenish  hue.  If  the  wafer  had  been  green,  the 
spot  seen  would  have  been  red. 


LIGHT. 


161 


151.  Color- Blindness.  —  In    some    persons    the   retina 
appears  to  be  affected  in  one  and  the  same  way  by  differ- 
ent colors,  or  even  by  all  colors.     The  most  common  form 
of  this  color-blindness •,  as  it  is  called,  is  an  inability  to  dis- 
tinguish red  and  green.     Thus  many  persons  cannot  dis- 
tinguish between  the  colors  of  the  leaves  of  the  cherry-tree 
and  its  fruit.     In  some  cases,  persons  who  were  thus  color- 
blind without  being  aware  of  it,  and  who  have  been  em- 
ployed on  railways,  have  mistaken  the  color  of  signal  lights, 
and  serious  accidents  have  been  the  result. 

This  blindness  may  arise  either  from  a  defect  in  the 
retina,  or  from  some  peculiarity  in  the  absorptive  powers 
of  the  humors  of  the  eye. 

152.  Single  Vision.  —  Since  an  image  is  formed  on  the 
retina  of  each  eye,  it  would  seem  that  we  ought  to  see  ob- 
jects double.     That  we  see  them  single  is  probably  owing 
to  the  way  in  which  the  eyes  are  connected  with  each 
other  and  with  the  brain.      This  connection  is  shown  in 
Figure  124.      It  will  be   seen 

that  a  part  of  the  optic  nerve 

runs  round  from   one  eye   to 

the    other,   and    a   part   from 

each  eye  to  each  side  of  the 

brain,  and  a  part  from  one  side 

of  the  brain  round  to  the  other. 

Each    eye   is   thus   connected 

with  the  other,  and  with  each 

side  of  the    brain,   and    these 

sides  are  connected  with  each 

other.     In   this  way  the  eyes 

are  virtually  a  single  eye,  the 

inner  side  of  the  one  corresponding  to  the  outer  side  of 

the  other ;  that  is,  each  point  to  the  left  of  the  middle  of 

one  eye  corresponds  to  a  point  situated  the  same  distance 

to  the  left  of  the  middle  of  the  other.      As  the  images 

K 


Fig.  124. 


1 62  LIGHT. 

are  always  formed  with  their  centres  at  the  centres  of  the 
eyes,  the  right  and  left  parts  of  the  images  will  be  on 
corresponding  parts  of  the  eyes,  and  they  will  therefore 
appear  as  one. 

If,  however,  by  pressing  the  finger  upon  the  eyeball,  or 
in  any  other  way,  we  cause  the  images  to  fall  upon  parts 
of  the  eye  which  do  not  correspond,  the  object  is  seen 
double.  Some  persons  always  see  double,  because  they 
cannot  direct  both  eyes  so  that  the  image  of  an  object 
shall  be  formed  about  the  centre  of  each. 

153.  The  Optical  Axis  and  the   Visual  Angle.  —  A  line 
drawn   from   the   centre  of  the  yellow  spot    through  the 
centre  of  the  pupil  is  called  the  optical  axis.     When  we 
look  at  any  object  we  must  turn  the  eye  so  as  to  direct 
this  axis  toward  it.     This   enables  us  to  appreciate  the 
direction  of  the  object. 

We  have  seen  that  the  image  of  a  candle  or  other  object, 
formed  by  a  convex  lens,  is  contained  between  lines  drawn 
from  the  extremities  of  the  object  through  the  centre  of 
the  lens.  In  the  same  way  the  image  of  an  object  on 
the  retina  is  contained  between  lines  drawn  from  the  ex- 
tremities of  the  object  through  the  centre  of  the  crystalline 
lens.  The  angle  contained  between  lines  thus  drawn  is 
called  the  visual  angle  of  the  object,  and  of  course  meas- 
ures the  length  of  the  image  on  the  retina.  All  objects 
which  have  the  same  visual  angle  form  images  of  the  same 
length  on  the  retina. 

154.  How  we  estimate  the  Size  of  a  Body.  — The  visual 
angle  evidently  gives  us  no  information  as  to  the  real  size 

Fig.  125. 


LIGHT.  163 

of  a  body;  for  we  see  from  Figure  125  that  the  visual 
angle  of  a  body  diminishes  as  its  distance  increases,  and 
also  that  bodies  at  different  distances  may  have  the  same 
visual  angle,  though  they  are  not  of  the  same  size.  Thus 
A  B  and  A1  B'  are  the  same  object,  but  A'  B'  which  is 
farther  off  has  the  smaller  visual  angle.  Again  C  D 
and  A'  B  have  the  same  visual  angle,  but  A  Br  is  the 
larger. 

We  must,  then,  know  the  distance  of  a  body  in  order  to 
estimate  its  size  ;  but  when  we  know  this  distance  we  esti- 
mate its  size  instinctively.  Thus  a  chair  at  the  farthest 
end  of  the  room  has  a  visual  angle  only  half  as  large  as  a 
chair  at  half  the  distance,  yet  we  cannot  make  it  seem 
smaller  if  we  try.  If  we  are  in  any  way  deceived  as  to 
the  distance  of  an  object  we  are  also  deceived  as  to  its 
size. 

155.  How  we  estimate  the  Distance  of  an  Object.  —  If  we 
refer  to  Figure  126,  we  see  that  when  the  eyes  are  directed 

Fig.  126. 


to  a  distant  object,  as  C,  they  are  turned  inward  but 
slightly ;  while  they  are  turned  inward  considerably  when 
directed  to  the  nearer  object  D.  The  muscular  effort  we 
have  to  make  in  thus  turning  the  eyes  inward  so  as  to 
direct  them  upon  an  object  is  one  of  the  best  methods  we 
have  of  estimating  its  distance. 

Again,  we  have  seen  that  we  have  to  adjust  the  eye  for 


1 64  LIGHT. 

different  distances,  and  the  effort  we  have  to  make  in  this 
adjustment  helps  us  to  judge  of  the  distance. 

We  also  judge  of  the  distance  of  an  object  from  the  dis- 
tinctness with  which  we  see  it  The  more  obscure  it  is, 
the  more  distant  it  seems.  It  is  for  this  reason  that  ob- 
jects seen  in  a  fog  sometimes  appear  enormously  large. 
They  appear  indistinct,  and  we  cannot  rid  ourselves  of  the 
impression  that  they  are  far  off;  and  hence  they  seem 
large,  though  they  may  really  be  small  and  near  us. 

The  celebrated  "  Spectre  of  the  Brocken,"  seen  among 
the  Hartz  mountains,  is  a  good  illustration  of  the  effect  of 
indistinctness  upon  the  apparent  size  of  an  object.  On  a 
certain  ridge,  just  at  sunrise,  a  gigantic  figure  of  a  man  had 
often  been  seen  walking,  and  extraordinary  stories  were 
told  of  him.  About  the  year  1800  a  French  philosopher 
and  a  friend  went  to  watch  the  spectre.  For  many  morn- 
ings they  looked  for  it  in  vain.  At  last,  however,  the 
monster  was  seen,  but  he  was  not  alone.  He  had  a  com- 
panion, and,  singularly  enough,  the  pair  aped  all  the  mo- 
tions and  attitudes  of  the  two  observers.  In  fact,  the  spec- 
tres were  merely  the  shadows  of  the  observers  upon  the 
morning  fog  which  hovered  over  the  valley  between  the 
ridges ;  and  because  the  shadows,  though  near,  were  very 
faint,  the  figures  seemed  to  be  distant,  and  like  gigantic 
men  walking  on  the  opposite  ridge. 

When  we  know  the  real  size  of  an  object  we  judge  of  its 
distance  from  the  visual  angle;  but  we  judge  of  the  distance 
of  unknown  objects  mainly  by  comparing  it  with  the  dis- 
tance of  known  objects.  This  is  one  reason  why  the  moon 
appears  larger  near  the  horizon  than  overhead,  though  she 
is  really  nearer  in  the  latter  case.  When  she  is  on  the 
horizon  we  see  that  she  is  beyond  all  the  objects  on  the 
earth  in  that  direction,  and  therefore  she  seems  farther  off 
than  when  overhead,  where  there  are  no  intervening  ob' 
jects  to  help  us  to  judge  of  the  distance. 


LIGHT.  165 

We  are  better  able  to  judge  of  the  distance  of  objects 
seen  horizontally  on  the  surface  of  the  earth,  where  we  are 
in  the  habit  of  walking  about,  than  when  we  see  them 
above  us.  In  the  latter  case  they  seem  nearer  and  conse- 
quently smaller  than  they  really  are.  Thus  the  vane  on  a 
church  spire,  a  hundred  feet  high,  may  be  five  or  six  feet 
long,  but  it  does  not  appear  half  that  length.  Again,  peo- 
ple on  the  top  of  a  lofty  building  appear  very  small,  while 
at  the  same  distance  from  us  on  the  surface  of  the  earth 
they  would  appear  of  the  ordinary  size. 

156.  Why  Bodies  near  us  appear  Solid.  —  Hold  any  solid 
object,  as  a  book,  about  a  foot  from  the  eyes,  and  look  at 
it  first  with  one  eye  and  then  with  the  other.     It  will  be 
seen  that  the  two  images  of  the  object  are  not  exactly 
alike.     With  the  right  eye  we  can  see  a  little  more  of  the 
right  side  of  the  object,  and  with  the  left  eye  a  little  more 
of  its  left  side.     It  seems  to  be  the  blending  of  these  two 
pictures  which  causes  objects  to  appear  solid. 

157.  The  Stereoscope. — The   principle  just   stated   ex- 
plains the  action  of  the  stereoscope. 

Two  photographs  of  an  object 
are  taken  from  slightly  different 
points  of  view,  so  as  to  obtain 
pictures  like  those  formed  in  the 
two  eyes.  These  photographs  are 
placed  before  the  eyes  in  such  a 
manner  that  each  eye  sees  only 
one,  but  both  are  seen  in  the  same 
position.  This  is  effected  by  the 
arrangement  shown  in  Figure  127. 
The  pictures  are  placed  at  A  and 
B.  The  rays  of  light  from  them 
fall  upon  the  lenses  m  and  «,  and 
in  passing  through  them  are  bent 
so  that  they  enter  the  eye  as  if 


1 66  LIGHT. 

they  came  from  the  direction  C.  The  lenses  are  por- 
tions of  a  double-convex  lens,  arranged  as  shown  in  the 
figure. 

158.  The  Laws  of  Distinct  Vision.  —  To  see  an  object 
distinctly,  a  clear  image  of  it  must  be  formed  on  the  retina. 
It  has  been  seen  that  the  eye  has  the  power  of  adjusting 
itself  so  as  to  form  distinct  images  of  objects  at  different 
distances.  When,  however,  an  object  is  brought  quite 
near  the  eye,  it  becomes  indistinct ;  showing  that  there  is 
a  limit  to  this  power  of  adjustment.  The  rays  are  now  so 
divergent  that  the  lens  cannot  bring  them  to  a  focus  on  the 
retina.  The  nearest  point  at  which  a  distinct  image  is 
formed  upon  the  retina  is  called  the  near  point  of  vision, 
and  the  greatest  distance  at  which  such  an  image  is  formed 
is  called  the  far  point.  In  perfectly  formed  eyes  the  near 
point  is  about  3^  inches  from  the  eye,  and  the  far  point  is 
infinitely  distant.  In  such  eyes  parallel  rays  are  brought 
to  a  focus  exactly  at  the  retina  when  the  eye  is  at  rest ; 
that  is,  when  the  crystalline  lens  is  of  its  natural  convexity. 
The  pupil  of  the  eye  is  so  small  that  the  rays  which  fall 
upon  it  from  objects  18  or  20  inches  distant  diverge  so 
little  that  they  may  be  regarded  as  parallel.  The  dis- 
tance of  the  near  and  far  points,  however,  is  not  the  same 
for  all  eyes.  In  some  cases,  the  near  point  is  consider- 
ably less  than  3^  inches  from  the  eye,  while  the  far  point 
is  only  eight  or  ten  inches.  In  other  cases  the  near  point 
is  twelve  inches  from  the  eye,  and  the  far  point  infinitely 
distant.  The  former  are  called  near-sighted  eyes ;  the 
latter,  far-sighted  ones. 

It  was  once  thought  that  near-sightedness  was  due  to 
the  too  great  convexity  of  the  cornea  or  the  crystalline 
lens,  or  of  both,  and  far-sightedness  to  the  too  slight  con- 
vexity of  the  same.  But  actual  measurement  has  shown 
that  their  real  cause  lies  in  the  shape  of  the  eyeball,  which 
in  far-sighted  people  is  flattened,  and  in  near-sighted  peo- 


LIGHT.  167 

pie  elongated,  in  the  direction  of  the  axis.     In  Figure  128 
the  curve  N  shows  the  form  of  the  normal,  or  perfect  eye  ; 

Fig.  128. 


Nf,  of  the  far-sighted  eye ;  and  N"t  of  the  near-sighted 
eye.  In  this  figure  the  eye  is  represented  as  at  rest,  and 
it  is  seen  that  the  parallel  rays  A  and  A  are  brought  to  a 
focus  on  the  retina  of  the  normal  eye,  while  only  the  con- 
vergent rays  A'  and  A'  are  brought  to  a  focus  on  the  retina 
of  the  far-sighted  eye,  and  only  the  divergent  rays  A"  on 
the  retina  of  the  near-sighted  eye. 

A"  then  is  the  far  point  for  the  near-sighted  eye,  since 
the  lens  has  now  its  least  convexity ;  and  this  point  must 
be  within  18  or  20  inches,  since  the  rays  from  an  object  at 
a  greater  distance  are  virtually  parallel  and  cannot  be 
brought  to  a  focus  on  the  retina.  The  near  point  must  be 
less  than  for  the  normal  eye,  since  the  retina  is  farther 
from  the  lens,  and  therefore  rays  of  greater  divergence  can 
be  brought  to  a  focus  upon  it.  In  the  far-sighted  eye  the 
retina  is  nearer  the  lens  than  in  the  normal  eye  ;  hence 
the  near  point  must  be  farther  away.  While  then  the 
normal  eye  sees  distant  objects  distinctly  without  adjust- 
ment, the  far-sighted  eye  must  adjust  itself  to  see  such 
objects. 

The  defect  of  far-sighted  eyes  can  be  in  great  measure 
remedied  by  wearing  convex  glasses,  which  help  to  bring 
the  rays  to  a  focus  on  the  retina,  and  thus  diminish  the 
distance  of  the  near  point.  The  defect  of  near-sighted 


1 68  LIGHT. 

eyes  can  be  remedied  by  the  use  of  concave  glasses,  which 
render  parallel  rays  divergent,  and  thus  increase  the  dis- 
tance of  the  far  point. 

The  first  law  of  distinct  vision,  then,  is  that  a  distinct 
image  of  the  object  must  be  formed  on  the  retina. 

Again,  it  is  well  known  that,  as  evening  approaches,  ob- 
jects become  indistinct.  Here,  of  course,  the  image  formed 
on  the  retina  is  distinct,  but  it  is  not  brilliant  enough  to 
produce  the  proper  effect  upon  the  optic  nerve. 

The  second  law  of  distinct  vision,  then,  is  that  the  image 
must  be  sufficiently  illuminated. 

Again,  some  objects  are  so  small  that  they  cannot  be 
seen,  however  much  they  may  be  illumined.  Here  the 
image  is  too  minute  to  affect  the  optic  nerve. 

The  third  law  of  distinct  vision,  then,  is  that  the  image 
must  be  of  sufficient  magnitude. 

159.  Old  Eyes.  —  As  the  eye  grows  old  it  loses  its 
power  of  adjustment,  the  crystalline  lens  becoming  less 
elastic.  Hence  old  eyes  can  see  distinctly  only  distant 
objects.  This,  however,  is  quite  a  different  thing  from 
far-sightedness.  In  the  far-sighted  eye  there  is  no  lack 
of  power  to  change  the  convexity  of  the  lens,  but  this 
power  becomes  useless  because  of  the  distance  of  the 
retina. 

This  defect  of  vision  caused  by  age  can  be  remedied 
by  the  use  of  convex  glasses. 

SUMMARY. 

The  camera  obscura  is  an  apparatus  by  which  an  image 
of  an  object  can  be  formed  on  a  screen  in  a  darkened 
chamber. 

The  chamber  may  be  filled  with  air,  water,  or  any  other 
transparent  substance.  (142.) 

The  eye  is  a  water  camera.     (143.) 


LIGHT.  169 

The  eye  adjusts  itself  to  light  of  varying  intensity  by 
varying  the  size  of  the  pupil.  (143.) 

It  adjusts  itself  to  various  distances  by  changing  the 
convexity  of  the  crystalline  lens.  (144.) 

The  optic  nerve  is  blind. 

The  luminous  vibrations  are  intercepted  by  the  rods  and 
cones •,  and  by  these  transmitted  to  the  optic  nerve.  (146.) 

Anything  which  excites  the  optic  nerve  produces  the 
sensation  of  light.  (147.) 

The  impression  on  the  retina  lasts  an  appreciable  lime 
after  the  object  which  produced  it  has  been  removed. 
(148.) 

The  impression  of  a  bright  object  extends  beyond  the 
image,  giving  rise  to  irradiation.  (149.) 

The  sensitiveness  of  the  retina  for  any  color  is  readily 
exhausted.  (150.) 

Many  people  are  color-blind.     (151.) 

The  eyes  are  so  connected  by  the  optic  nerve  that  we 
see  objects  single,  though  an  image  is  formed  on  each 
retina.  (152.) 

We  judge  of  the  direction  of  an  object  by  the  direc- 
tion of  the  axis  of  the  eye  when  turned  towards  it. 

The  visual  angle  of  an  object  depends  on  its  size  and 
distance.  (153.) 

We  judge  of  the  size  and  distance  of  an  object  by 
means  of  its  visual  angle,  the  direction  of  the  optical 
axes,  the  distinctness  of  the  image,  and  the  effort  we  have 
to  make  to  adjust  the  eye  for  seeing  it.  (154,  155.) 

Near  bodies  seem  solid,  because  the  images  in  the  two 
eyes  are  not  exactly  alike.  (156.) 

The  stereoscope  causes  pictures  on  a  plane  surface  to 
appear  solid.  (157.) 

In  order  that  vision  may  be  distinct,  a  distinct  image 
must  be  formed  on  the  retina,  the  image  must  be  suffi- 
ciently illuminated,  and  must  have  sufficient  magnitude. 
8 


1  70  LIGHT. 

Perfect  eyes  can  adjust  themselves  to  any  distance  from 
3j  inches  to  infinity. 

Near-sighted  eyes  can  adjust  themselves  only  to  short 
distances,  and  far-sighted  eyes  only  to  long  distances. 


Eyes  lose  their  power  of  adjustment  as  they  grow  old. 


Near-sightedness  and  far-sightedness  are  due  to  defec- 
tive forms  of  the  eyeball.  These  defects  and  that  caused 
by  age  can  be  partially  remedied  by  the  use  of  glasses. 
(158,  I59-) 

THE   MICROSCOPE  AND  THE  TELESCOPE. 

1  60.  The  Simple  Microscope.  —  We  have  seen  that  an 
object  must  form  upon  the  retina  an  image  of  a  certain 
magnitude,  in  order  to  be  distinctly  seen.  Now  the  mag- 
nitude of  the  image  may  be  increased  indefinitely  by 
bringing  the  object  nearer  the  eye  ;  but  when  it  is  brought 
too  near,  the  eye  is  not  able  to  bring  the  rays  from  it  to  a 
focus  on  the  retina.  We  may  accomplish  this,  however, 
by  the  aid  of  a  convex  lens.  Such  a  lens  is  the  simplest 
form  of  a  microscope.  It  is  called  a  microscope  (from  two 
Greek  words  meaning  to  see  small  things)  because  it  en- 
ables us  to  see  things  smaller  than  the  unaided  eye  can 
distinguish.  The  more  convex  the  lens,  the  nearer  can 
the  object  be  brought  to  the  eye,  and  the  larger  will  be 
the  image  on  the  retina. 

1  6  1.  The  Compound  Microscope.  —  In  Figure  129  we 
have  what  is  called  a  compound  microscope.  M  is  a  lens  ; 
A  B  is  an  object  placed  near  it.  An  enlarged  image  of 
A  B  is  formed  at  a  £,  and  this  image  is  viewed  through  the 
lens  JVj  in  the  same  way  that  an  object  is  viewed  with  the 
single  lens  of  a  simple  microscope. 

The  greater  magnifying  power  of  this  microscope  is  due 


LIGHT. 


to  the  fact  that  we  examine,  not  the  object  itself,  but  an 
enlarged  image  of  it. 

Fig.  129. 


The  lens  Mis  called  the  object-glass  or  the  objective;  and 
N,  the  eye-piece.  The  latter  is  usually  a  combination  of 
two  lenses. 

We  have  seen  that  a  convex  lens  causes  the  rays  pass- 
ing through  it  to  meet  at  a  point  called  the  focus.  In 
reality,  however,  this  focus  is  not  exactly  the  same  for 
all  the  rays.  Those  falling  near  the  margin  of  the  lens 
meet  a  little  sooner  than  those  falling  upon  its  centre, 
giving  rise  to  what  is  called  aberration.  The  more  convex 
the  lens,  the  greater  the  aberration,  and  the  more  indis- 
tinct the  image. 

This  aberration  can  be  diminished  by  diminishing  the 
size  of  the  lens,  so  that  all  the  rays  must  fall  near  its  cen- 
tre. For  this  reason  the  objective  of  a  compound  micro- 
scope, which  is  a  very  convergent  lens,  is  made  very  small. 

The  magnifying  power  of  a  microscope  is  commonly  ex- 
pressed in  diameters.  If  it  makes  the  breadth  of  the  object 
appear  50  times  as  great  as  it  really  is,  it  is  said  to  mag- 
nify 50  diameters.  Of  course  the  surface  of  the  object  is 
increased  as  the  square  of  its  diameter;  or  in  this  case 
2,500  times.  The  most  powerful  compound  microscopes 
magnify  1,500  diameters,  or  even  more. 

Of  course  there  is  no  more  light  on  this  enlarged  image 
than  there  is  on  the  object  itself;  hence  the  object  must 
be  very  strongly  illuminated  in  order  that  the  light  when 
thus  diluted  may  be  sufficient  to  affect  the  eye. 


172  LIGHT. 

162.  The  Telescope.  —  As  an  object  is  moved  farther  and 
farther  from  the  eye,  its  image  becomes  smaller  and 
smaller,  until  at  last  it  may  cease  to  affect  the  eye,  even 
though  the  object  itself  may  be  very  large.  An  instrument 
for  examining  distant  objects  is  called  a  telescope.  Its 
essential  parts  are  shown  in  Figure  130.  The  word  is 

Fig.  130. 


made  up  of  two  Greek  words  meaning  to  see  far  off.  Its 
construction  is  very  much  like  that  of  the  compound  mi- 
croscope. It  has  an  object-glass  for  forming  an  image  of 
the  object,  and  an  eye-piece  for  examining  this  image.  It 
differs  from  the  microscope  mainly  in  the  fact  that  the 
image  is  always  smaller  than  the  object.  Since  the  object 
is  very  distant,  the  rays  which  fall  upon  the  object-glass 
are  virtually  parallel,  and,  therefore,  this  glass  may  have  a 
great  diameter  without  making  the  image  indistinct  through 
aberration.  The  larger  the  diameter  the  better,  since  it 
will  collect  and  concentrate  the  more  light  on  the  image. 
The  object-glass  of  the  great  telescope  in  the  Observatory 
at  Cambridge,  Mass.,  is  15  inches  in  diameter.  The  tele- 
scope in  the  Observatory  at  Chicago,  Illinois,  has  an  ob- 
ject-glass 18  inches  in  diameter.  This  instrument  was 
made  by  Alvan  Clark  &  Sons  of  Cambridge,  and  is  consid- 
ered the  best  telescope  in  the  world.  Such  an  instrument 
takes  in  as  much  light  as  the  eye  would  if  its  pupil  were  18 
inches  in  diameter ;  that  is,  since  the  pupil  of  the  eye  is 
not  more  than  a  quarter  of  an  inch  in  diameter,  (4  X  i8)9 
times  as  much  light. 


LIGHT. 


173 


The  size  of  the  image  increases  with  its  distance  from 
the  object-glass.  That  this  distance  may  be  as  great  as 
possible,  the  object-glass  has  very  slight  convexity. 

We  now  see  how  the  object-glass  of  the  telescope  dif- 
ers  from  that  of  the  microscope.  The  former  is  made 
as  large  as  possible,  with  very  slight  convexity ;  while  the 
latter  is  made  as  small  as  possible,  with  very  great  con- 
vexity. 

The  eye-piece  is  the  same  in  both  instruments.  The 
magnifying  is  chiefly  done  by  the  eye-piece. 

We  have  seen  that  light  is  dispersed  when  passing 
through  a  prism  (100),  so  as  to  form  the  spectrum.  Now 
the  edge  of  a  lens  is  like  the  refracting  angle  of  a  prism, 
and  therefore  disperses  the  light  which  passes  through  it, 
giving  rise  to  colored  fringes  round  the  image.  This  can 
be  prevented  by  the  use  of  a  second  lens  made  of  glass  of 
different  dispersive  power.  A  lens  thus  cor- 
rected is  called  an  achromatic  (colorless)  lens, 
and  is  shown  in  Figure  131.  The  second  lens 
A  acts  just  as  the  second  prism  does  in  Figure 

75- 

163.    The  Terrestrial  Telescope.  —  Of  course 
the  image  in  the  telescope  described  above  will 
be  inverted.    This  makes  no  difference  when  we 
are  looking  at  the  heavenly  bodies,  but  is  an  inconvenience 
in  viewing  terrestrial  objects.     An  erect  image  may  be  ob- 


Fig.  132. 


tained  by  using  additional  lenses,  as  shown  in  Figure  132. 
The  first  inverted  image  is  formed  at  a  b.      The  lens  P 


174  LIGHT. 

renders  the  rays  diverging  from  this  image  parallel,  and 
the  lens  Q  brings  them  to  a  focus  again  at  of  b '.  These 
two  lenses  then  act  as  one,  and  form  an  inverted  image  of 
the  inverted  image,  which  will  be  an  erect  image. 

164.   The  Opera-Glass. — The  lenses  used  in  the  opera- 
glass  are  shown  in  Figure  133.     M  is  the  object-glass,  and 


is  a  converging  lens.  R  is  the  eye-piece,  and  is  a  diverging 
lens.  The  rays  of  light  coming  from  the  ends  A  and  B  of 
the  object  would  be  brought  to  a  focus  at  a  b,  where  an 
inverted  image  would  be  formed.  But  on  falling  upon  the 
eye-piece  R  they  are  turned  aside,  as  shown  in  the  figure, 
so  that  they  enter  the  eye  as  if  they  came  from  the  points 
a'  and  b'.  Hence  the  eye  sees  the  object  A  B  erect  and 
under  a  greater  visual  angle  than  if  it  had  been  viewed 
directly ;  so  that  the  object  appears  larger  than  it  would 
without  the  aid  of  the  instrument. 

The  telescope  invented  by  Galileo  was  an  opera-glass. 

THE   MAGIC   LANTERN. 

165.  In  the  photographic  camera  (Figure  134)  a  small 
inverted  image  of  the  object  is  formed  upon  the  glass 
screen  E.  We  will  now  suppose  this  image  to  be  a  trans- 
parent picture,  and  that  a  strong  light  is  sent  through  it 
from  behind.  An  enlarged  and  upright  image  of  the 
picture  will  be  formed  by  the  lenses  in  the  tube  A,  and 
may  be  received  upon  a  screen.  The  nearer  the  pic- 
ture is  to  the  lens,  the  farther  off  and  the  larger  will  be 
the  image. 


LIGHT. 


175 


An  instrument  for  thus  projecting  pictures  upon  a  screen 
is  called  a  magic  lantern. 

Fig.  134. 


If  the  picture  is  greatly  enlarged,  it  is  necessary  to  use  a 
strong  light.  The  calcium  light,  the  magnesium  light,  the 
electric  light,  and  solar  light  are  best  adapted  to  the  pur- 
pose. For  small  lanterns  and  a  small  screen  an  oil-lamp 
with  a  reflector  may  be  used. 

When  the  picture  is  very  small,  it  must  be  placed  very 
near  the  lens  in  order  that  a  large  image  may  be  thrown 

Fig.  135- 


176  LIGHT. 

upon  the  screen.  In  this  case,  as  in  that  of  the  compound 
microscope,  the  lens  must  be  very  small  and  very  convex. 
The  instrument  thus  arranged  is  called  a  solar  microscope, 
and  is  shown  in  Figure  135.  M  is  a  mirror  which  throws 
the  solar  rays  into  the  tube  of  the  microscope,  where  the 
lenses  /  and  o  condense  them  upon  the  object  at  m.  The 
small  lens  x  then  brings  the  rays  to  a  focus  at  a  b. 

SUMMARY. 

The  microscope  is  an  instrument  which  enables  the  eye 
to  see  an  object  at  less  distance  than  it  otherwise  could. 

With  the  simple  microscope  the  object  is  viewed  directly; 
with  the  compound  microscope  an  enlarged  image  of  the 
object  is  viewed.  (160,  161.) 

The  telescope  is  an  instrument  for  viewing  a  distant  ob- 
ject. A  bright  image  of  the  object  is  formed  in  the 
focus  of  the  object-glass  and  viewed  with  a  microscope. 

In  a  compound  microscope  the  image  is  always  larger 
than  the  object  ;  in  the  telescope,  it  is  always  smaller. 


The  object-glass  of  a  telescope  is  rendered  achromatic 
by  combining  two  lenses  of  different  dispersive  power. 
(162.) 

In  terrestrial  telescopes  two  or  more  lenses  are  combined 
so  as  to  make  the  object  appear  upright.  (163.) 

In  the  opera-glass,  the  object-glass  is  a  converging  lens, 
and  the  eye-piece  a  diverging  lens.  (164.) 

The  magic  lantern  and  solar  microscope  are  instruments 
for  throwing  a  magnified  image  of  an  object  upon  a  screen 
in  a  darkened  room.  (165.) 


LIGHT.  177 


MIRRORS. 

1 66.  Plane  Mirrors.  —  Any  smooth  reflecting  surface  is 
called  a  mirror.     If  the  surface  is  flat,  it  is  called  a  plane 
mirror. 

In  Figure  136  suppose  a  point  of  light  A  to  be  in  front 

of  the  plane  mirror  N M.    The  rays 

diverging  from  A,  as  A  B  and  A  C 

are  reflected  from  the  mirror  so  as 

to  make  the  angle  of  reflection  equal 

to  that  of  incidence.      After  reflec- 
tion they  enter  the  eye  O  just  as  if 

they  came  from  the  point  a.      This 

point  will   therefore    appear   to    be 

just  as  far  behind  the  mirror  as  A 

is  in  front  of  it. 

Suppose  the  arrow  A  B  (Figure  137)  to  be  placed  in 

front  of  the  mirror.  The 
rays  diverging  from  A  will, 
after  reflection,  enter  the 
eye  as  if  they  came  from 
a;  those  diverging  from 
B,  as  if  they  came  from 
b;  and  those  which  come 
from  points  between  A 
and  B,  as  if  they  came 
from  corresponding  points 

between  a  and  b.      Hence   the   arrow  will   appear  to  be 

as  far  behind  the  mirror  as  it  really  is  in  front  of  it. 

167.  Multiple  Images   in   Plane   Mirrors.  —  If  a  light 
be    placed   in    front  of  a  looking-glass,  as  at  A  (Figure 
138)  and  an  observer  look  at  it  in  the  mirror  from  the 
direction  H,  he  sees  two  lights,  one  at  a  and  the  other 
at  a.      A  part  of  the  light  is  reflected  from  the  upper 

8*  L 


1 78  LIGHT. 

Fig.  138.  surface  of  the  mirror   in  the  direc- 

tion b  E,  and  enters  the  eye  as  if 
it  came  from  a.  Another  part  is 
reflected  at  c,  and,  on  being  refracted 
at  d,  enters  the  eye  as  if  it  came 
from  a1. 

If  two  mirrors  be  placed  at  right 
angles,  as  shown  in  Figure  139,  and 
a  light  be  placed  at  O,  three  im-  p. 

ages  of  the  light  will  be  seen. 
A  part  of  the  rays  from  O,  re- 
flected at  C,  enter  the  eye  as  if 
they  came  from  O1;  another  part, 
reflected  from  Z>,  as  if  they  came 
from  O" ;  and  another  part,  twice 
reflected,  at  A  and  B,  as  if  they 
came  from  O"'. 

By  placing  the  mirrors  at  dif- 
ferent angles,  a  variety  of  images 
may  be  obtained.  Their  number  and  their  arrangement 
(which  will  always  be  symmetrical)  will  depend  upon  the 
angle  at  which  the  mirrors  are  placed.  The  kaleidoscope, 
invented  by  Sii*  David  Brewster,  depends  upon  this  effect 
of  inclined  mirrors.  It  consists  of  a  tube  in  which  there 
are  three  mirrors  inclined  at  an  angle  of  60°.  One  end  of 
the  tube  is  closed  with  a  piece  of  ground  glass,  and  the 
other  end  with  a  cap  in  which  there  is  a  small  opening. 
Small  irregular  pieces  of  colored  glass  are  placed  between 
the  ground  glass  and  another  glass  disc.  On  looking  into 
the  tube,  these  objects  and  their  images  seem  arranged  in 
beautiful  and  symmetrical  forms,  which  continually  change 
as  the  tube  is  turned  round. 

1 68.   Concave  Mirrors.  —  A  concave  mirror  is  a  portion 
of  a  spherical  surface  viewed  from  within. 

The  action  of  such  a  mirror  upon  parallel  rays  is  shown 


LIGHT. 


179 


in  Figure  140.     Cis  the  centre  of  the  sphere  of  which  the 
mirror  is  a  part.      The  radii  C  A,  C  B,  and  C  D  are  of 

Fig.  140. 


course  perpendicular  to  the  surface  of  the  mirror  at  the 
points  A,  B,  and  D.  The  parallel  rays  H,  G,  and  Z,  on 
meeting  the  mirror,  are  reflected  so  as  to  make  the  angle 
of  reflection  equal  to  that  of  incidence ;  that  is,  making 
C  B  H  equal  to  C  B  F,  C  D  G  to  C  D  F,  etc.  Hence 
the  reflected  rays  are  made  to  converge.  If  the  mirror  is 
not  more  than  8°  or  10°  in  breadth,  the  rays  will  all  meet 
at  F,  half-way  between  C  and  A.  This  point  is  called  the 
principal  focus  of  the  mirror. 

Fig.  141. 


Figure  141  shows  the  action  of  a  concave  mirror  upon 
diverging  rays.  The  rays  diverging  from  the  point  L  meet 
the  mirror  at  a  smaller  angle  of  incidence  than  if  they 
were  parallel,  and  their  angles  of  reflection  will  also  be 
less.  They  will  therefore  meet  at  a  point,  /,  farther  from 
the  mirror  than  the  principal  focus  is.  If  the  luminous 
point  were  at  /,  the  rays  would  be  brought  to  a  focus  at  L. 
The  points  L  and  /  are  called  conjugate  foci. 

As  L  approaches  C,  I  also  approaches  it,  until  at  C  the 


i8o 


LIGHT. 


two  coincide.  As  L  recedes  from  C,  /  approaches  F;  until 
L  is  removed  so  far  that  the  rays  become  sensibly  parallel, 
when  /  coincides  with  F.  If  L  is  at  F,  the  reflected  rays 
will  be  parallel ;  if  L  is  inside  F,  they  will  be  divergent, 
but  less  divergent  than  on  meeting  the  mirror. 

If  a  candle  AB  (Figure  142)  be  placed  before  a  con- 
Fig.  142. 


cave  mirror,  the  rays  diverging  from  A  are  brought  to  a 
focus  at  a ;  those  from  B,  at  b ;  and  those  from  points  be- 
tween A  and  B,  at  corresponding  points  between  a  and  b. 
So  long  as  A  B  is  to  the  left  of  C,  the  image  will  be  small- 
er than  the  object;  when  AB  is  to  the  right  of  C,  the 
image  will  be  larger  than  the  object ;  and  in  both  cases  it 
will  be  inverted.  If,  however,  the  candle  is  inside  the 
principal  focus,  it  will  be  seen  reflected  in  the  mirror,  up- 
right and  enlarged,  since  the  rays  are  rendered  less  diver- 
gent on  leaving  the  mirror. 

169.   Convex  Mirrors.  —  A  convex  mirror  is  a  portion  of 
the  surface  of  a  sphere  viewed  from  without 

Fig-  143- 


Such  a  mirror  renders  parallel  rays  divergent,  and  diver- 
gent rays  more  divergent  (Figure  143).  Hence  an  ob- 
ject reflected  in  it  appears  smaller  than  it  really  is. 


LIGHT. 


1 70.  The  Reflecting  Telescope.  —  A  concave  mirror  may  be 
used  instead  of  the  object-lens  of  a  telescope,  as  is  showr, 
in  Figure  144.  The  rays  from  an  object  falling  upon  the 

Fig.  144. 


Fig.  i45 


concave  mirror  M  are  reflected  so  as  to  form  an  image 
at  the  focus,  and  this  image  is  viewed  with  the  eyepiece  o. 
As  the  image  here  is  formed  by  reflected  light  the  instru- 
ment is  called  a  reflecting  telescope.  The  ordinary  tele- 
scope is  called  a  refracting  telescope,  since  the  image  is 
formed  by  refracted  light. 

The  largest  reflecting  telescope  ever  made  is  the  cele- 
brated one  of  Lord  Rosse,  which  has  a  diameter  of  6  feet 
and  a  focal  length  of  53  feet. 

171.  Parabolic  Mirrors. — The  mirror  shown  in  Figure 
145  has  what  is  called  a 
parabolic  surface,  and  is 
therefore  called  a  para- 
bolic mirror.  The  point  F 
is  called  the  focus,  and  the 
line  A  X  the  axis,  of  the 
mirror.  If  parallel  rays  be 
allowed  to  fall  upon  such 
a  mirror,  they  are  reflected 
exactly  to  the  focus  F, 
whatever  may  be  the  breadth  of  the  mirror.  On  the  other 
hand,  if  a  light  be  placed  at  the  focus,  its  rays  will  be 
reflected  from  the  mirror  in  parallel  lines.  This  is  be- 


1 82  LIGHT. 

cause  the  curvature  of  a  parabolic  surface  is  such  that  if 
a  perpendicular  be  drawn  to  any  point,  as  M,  the  angle 
which  it  makes  with  the  line  M  L,  drawn  parallel  to  the 
axis,  is  equal  to  the  angle  it  makes  with  the  line  M  F 
drawn  to  the  focus. 

Parabolic  mirrors  are  used  for  the  lanterns  placed  in 
front  of  locomotive  engines  and  in  many  light-houses. 

SUMMARY. 

Any  smooth  reflecting  surface  is  called  a  mirror. 

When  the  surface  is  flat,  it  is  called  a  plane  mirror  ;  when 
it  is  curved,  a  concave  or  convex  mirror.  (166,  168.) 

An  object  is  seen  reflected  in  a  plane  mirror  without 
enlargement,  but  it  appears  as  far  behind  the  mirror  as  it 
really  is  before  it.  (166.) 

In  a  convex  mirror  an  object  appears  smaller,  and  in  a 
concave  mirror  larger,  than  it  really  is.  (168,  169.) 

An  inverted  image  of  an  object  is  formed  in  the  focus 
of  a  concave  mirror.  (168.) 

A  concave  mirror  may  be  used  in  place  of  the  object- 
glass  in  a  telescope.  (170.) 

A  parabolic  mirror  renders  the  rays  which  diverge  from 
its  focus  parallel.  (171.) 

PHOTOGRAPHY. 

172.  The  Chemical  Action  of  Light.  —  If  a  surface  coated 
with  chloride  or  iodide  of  silver  be  exposed  to  light,  it 
gradually  blackens.  The  stronger  the  light,  the  more 
rapidly  the  change  of  color  takes  place.  There  are  many 
other  chemical  substances  which  are  more  or  less  affected 
by  the  action  of  light.  In  some  cases  the  light  does  not 
actually  decompose  the  substance,  but  gives  it  a  disposition 
to  break  up. 

This  chemical  action  of  light  is  the  basis  of  the  art  of 
photography. 


LIGHT.  183 

173.  The  Daguerreotype.  —  If  the  image  in  the  camera 
obscura  (142)  be  allowed  to  fall  for  a  short  time  upon  a 
copper  plate  coated  with  iodide  of  silver,  and  the  plate 
be  removed  and  examined,  no  change  appears  to  have 
taken  place.  If,  however,  the  plate  be  now  exposed  to 
the  vapor  of  mercury,  an  image  appears  exactly  like  that 
formed  in  the  camera.  The  mercury  condenses  upon  those 
parts  of  the  plate  which  have  been  most  strongly  illu- 
mined, and  thus  develops  the  picture  which  before  was 
latent.  If  this  plate  were  now  exposed  to  the  light,  the 
remaining  iodide  of  silver  would  blacken  so  as  to  obliter- 
ate the  picture.  But  if  the  iodide  be  dissolved  and  washed 
off  by  a  solution  of  hyposulphite  of  sodium,  the  picture  is 
fixed.  This  process  of  obtaining  pictures  by  means  of 
light  was  discovered  in  1839  by  a  Frenchman  named 
Daguerre,  and  from  him  the  pictures  are  called  daguerre- 
otypes. 

The  theory  of  the  daguerreotype  process  is  thus  stated 
by  Miller *:- 

"  Under  the  influence  of  light,  the  superficial  layer  of 
iodide  of  silver  is  modified  so  as  to  render  it  susceptible 
of  decomposition.  When  the  plate  is  acted  upon  by  the 
mercurial  vapor,  the  iodine  is  driven  to  the  deeper  layer  of 
silver,  and  a  film  of  silver  is  liberated  upon  the  surface  of 
those  parts  which  have  been  exposed  to  the  action  of  light, 
the  thickness  of  this  film  varying  with  the  intensity  and 
duration  of  the  light.  The  reduced  silver  combines  with 
the  mercury,  and  a  film  of  silver  amalgam  is  formed,  which 
varies  in  thickness  with  the  thickness  of  the  silver  film,  in 
consequence  of  which  the  reflected  tints  differ  according 
to  the  varying  thickness  of  this  film  :  those  parts  of  the 
iodized  plate  which  have  not  been  exposed  to  the  light 
of  course  do  not  combine  with  the  mercury.  After  the 
plate  has  been  treated  with  hyposulphite  of  sodium,  the 
*  Elements  of  Chemistry  (3d  Edition),  Part  II.,  page  895. 


184  LIGHT. 

excess  of  iodide  of  silver  is  removed,  and  the  blacks  con- 
sist of  metallic  silver.  Experiment  proves  that  those 
parts  of  the  plate  immediately  beneath  the  highest  lights 
are  more  deeply  corroded  than  the  others  by  the  action 
of  the  iodine  which  has  been  driven  inward  during  the 
process  of  mercurialization. 

"  In  complete  accordance  with  the  foregoing  explanation 
is  a  curious  fact  first  pointed  out  by  Mr.  Shaw,  —  that  if  a 
plate,  after  it  has  received  the  impression  in  the  camera, 
but  before  it  has  been  mercurialized,  be  exposed  to  the 
vapor  of  iodine  or  of  bromine  for  a  few  seconds,  the  image 
is  completely  effaced,  and  is  no  longer  producible  by 
mercury." 

174.  The  Collodion  Process.  —  This  process,  which  is  the 
one  now  almost   universally   employed,  was  invented  by 
Mr.  Archer,  in  1851.     A  solution  of  gun-cotton  in  ether 
is  impregnated  with  a  small  quantity  of  iodide  of  potas- 
sium or  cadmium,  forming  what  is  -called  iodized  collodion. 
A  film  of  this  is  spread  on  a  plate  of  glass,  which  is  then 
immersed  in  a  solution  of  nitrate  of  silver.     The  collodion 
film  thus   becomes  coated  with   yellow  iodide  of  silver, 
which  is  very  sensitive  to  light.     The  plate  thus  prepared 
requires  an  exposure  of  only  a  few  seconds  in  the  camera 
to  produce  the  latent  image,  which  is  afterwards  developed 
by  pouring  over  the  surface  a  weak  solution  of  pyrogallic 
acid  mixed  with  acetic  acid.      A  solution  of  ferrous  sul- 
phate is  also  often  used  for  the  same  purpose.     The  image 
is  r\Qvjjixed,  as  described  above,  by  pouring  over  the  plate 
a  solution  of  hyposulphite  of  sodium  or  of  cyanide  of  po- 
tassium.    The  negative  picture  thus  obtained  can  then  be 
employed  for  printing  a  positive,  as  explained  in  the  next 
section. 

175.  Photographic  Printing.  —  In  1839  Mr.  Fox  Talbot 
of  England  discovered  the  process  now  known  as  photo- 
graphic printing.     "  It  consisted  in  soaking  ordinary  writ- 


LIGHT.  185 

ing-paper  in  a  weak  solution  of  common  salt,  and,  when 
dry,  washing  it  over  upon  one  side  with  a  solution  of 
nitrate  of  silver,  consisting  of  one  part  of  a  saturated  solu- 
tion of  nitrate  with  6  or  8  parts  of  water.  This  operation 
was  performed  by  candle-light,  and  the  paper  was  dried 
at  the  fire ;  in  this  manner  a  film  of  chloride  of  silver, 
mixed  with  an  excess  of  nitrate  of  silver,  was  formed  upon 
the  surface  of  the  paper.  Suppose  that  it  were  desired  to 
obtain  a  copy  of  an  engraving,  or  of  the  leaf  of  a  tree : 
one  of  the  sheets  so  prepared  was  laid  under  the  engraving 
or  the  leaf  which  was  to  be  copied ;  the  two  were  pressed 
firmly  together  between  two  plates  of  glass,  and  exposed  to 
the  direct  rays  of  the  sun,  or  even  to  diffused  daylight,  for 
a  period  of  half  an  hour  or  an  hour.  The  impression  thus 
obtained  was  a  negative  one,  that  is  to  say,  the  shadows 
were  represented  by  lights,  and  the  lights  by  shadows  ;  those 
portions  of  the  surface  which  had  been  exposed  to  the 
strongest  light  becoming  dark,  and  the  parts  correspond- 
ing to  the  deep  shadows  in  the  engraving  remaining  white. 
The  pictures  were  then  fixed  by  immersing  them  in  a 
strong  solution  of  common  salt.  Considerable  improve- 
ments have  been  introduced  into  this  process  since  it  was 
first  published,  but,  in  principle,  this  operation,  which  has 
been  termed  photographic  printing,  remains  unchanged." 
(Miller.) 

Of  course,  when  negative  pictures  are  copied  by  this  pro- 
cess, positive  ones  (or  those  having  the  proper  distribution 
of  light  and  shade)  are  obtained. 

176.  Chemical  Action  of  the  Solar  Spectrum.  —  If  a  pure 
solar  spectrum  be  allowed  to  fall  upon  a  sheet  of  sensitive 
paper,  it  will  be  soon  seen  that  the  chemical  action  is  not 
uniformly  distributed  over  the  luminous  image.  The  maxi- 
mum of  light  falls  in  the  yellow  rays  about  Fraunhofer's 
line  Z>,  while  that  of  chemical  action  occurs  in  the  blue 
portion  of  the  spectrum  near  the  line  G,  about  one  third 


i86 


LIGHT. 


of  the  way  between  that  line  and  H.  The  blackening 
effect  extends  nearly  to  F  in  the  green,  while  it  is  pro- 
longed beyond  the  violet  end  of  the  spectrum  a  distance 
nearly  equal  to  two  thirds  of  the  length  of  the  luminous 
spectrum,  the  chemical  effect  gradually  shading  off  until  it 
is  imperceptible.  The  maximum  point,  however,  varies 
with  the  preparation  used.  With  the  Talbotype  iodized 
paper,  the  greatest  blackening  is  found  on  the  extreme 
limit  of  the  violet  ray.  When  bromide  of  silver  is  the  sen- 
sitive material,  the  chemical  action  is  prolonged  towards 
the  red  rays.  When  chloride  of  gold  is  used,  the  maxi- 
mum is  found  between  the  green  and  the  blue  rays,  and 
the  chemical  action  does  not  extend  beyond  the  violet 
more  than  half  as  far  as  when  the  salts  of  silver  are  used. 
In  Figure  146,  i  represents  the  space  occupied  by  the 


F   E 


luminous  spectrum  on  white  paper ;  2,  the  chemical  spec- 
trum on  bromide  of  silver ;  3,  the  Talbotype  spectrum. 

Inactive  spaces  occur  in  the  chemical  spectrum,  which, 
as  Becquerel  and  Draper  have  shown,  correspond  exactly 
with  the  dark  lines  found  in  the  visible  spectrum ;  but  they 
extend  also  into  the  prolongation  beyond  the  violet,  and 
occur  there  in  great  numbers.  These  fixed  lines  may  be 
obtained  upon  Talbotype  paper,  or,  better  still,  upon  a 
surface  of  collodion. 


LIGHT.  187 


SUMMARY. 

Light  either  causes  certain  chemical  compounds  to 
decompose  or  gives  them  a  disposition  to  do  so.  (172.) 

Hence  light  can  be  made  to  fasten  upon  properly  pre- 
pared surfaces  the  images  which  fall  upon  them  in  the 
camera.  (173.) 

The  daguerreotype  process  was  discovered  by  Daguerre, 
in  1839  ;  photographic  printing,  by  Talbot,  in  the  same 
year;  the  collodion  process,  by  Archer,  in  1851.  (173-175.) 

The  most  refrangible  rays  of  the  spectrum  have  the  most 
powerful  chemical  action. 

The  chemical  spectrum  extends  beyond  the  luminous 
spectrum  at  the  violet  end,  and  has  blank  spaces.  These 
spaces  correspond  to  Fraunhofer's  lines,  which  are  also 
chemically  inactive.  (176.) 

CONCLUSION. 

A  luminous  body  sends  out  light  in  every  direction, 
which  diminishes  in  intensity  as  the  square  of  the  distance 
increases.  These  rays  of  light  traverse  space  in  straight 
lines,  and  with  a  velocity  of  about  190,000  miles  a  second. 

When  rays  of  light  meet  a  different  medium  from  that 
through  which  they  have  been  passing,  they  are  partially 
reflected  and  partially  transmitted.  The  reflected  portion 
is  either  diffused  or  else  reflected  regularly.  In  the  latter 
case  the  angle  of  reflection  always  equals  the  angle  of  in- 
cidence. The  transmitted  portion  is  refracted  towards  or 
from  a  perpendicular  to  the  surface,  according  as  the  new 
medium  is  more  or  less  dense  than  the  old  one. 

In  passing  through  a  prism  a  ray  of  light  is  twice  re- 
fracted in  the  same  direction,  and  also  dispersed  into  a 
colored  band,  called  the  spectrum ',  which  differs  in  length 


l88  LIGHT. 

with  the  material  of  the  prism.  This  dispersion  shows  that 
a  ray  of  white  light  is  really  a  bundle  of  rays  of  different 
colors  and  of  different  refrangibility.  The  rays  of  white 
light  are  continually  sifted  as  they  fall  upon  bodies,  each 
body  absorbing  some  particular  color  or  colors,  and  trans- 
mitting or  dispersing  the  others.  It  is  this  which  gives 
bodies  their  color. 

Incandescent  solids  give  out  rays  of  all  the  prismatic 
colors,  but  incandescent  gases  give  out  rays  of  only  partic- 
ular colors.  By  means  of  the  spectroscope  we  can  ana- 
lyze the  light  emitted  by  an  incandescent  gas,  and  find  out 
the  elements  of  which  it  is  composed.  A  gas  absorbs  the 
same  rays  that  it  emits  when  incandescent. 

When  examined  with  the  spectroscope,  solar  and  stellar 
light  give  spectra  crossed  by  dark  lines.  Such  spectra 
show  that  the  light  comes  from  a  solid  or  liquid  nucleus, 
surrounded  by  a  gaseous  envelope,  and  enable  us  to  find 
what  elements  exist  in  these  envelopes. 

Rays  of  light  interfere  in  such  a  way  as  to  show  that 
light  is  propagated  by  means  of  waves.  These  waves  are 
exceedingly  minute,  and  are  longest  in  red,  and  shortest  in 
violet  light.  Difference  in  color  is  then  analogous  to  dif- 
ference in  pitch,  the  difference  in  both  cases  being  caused 
by  a  difference  in  the  rapidity  of  vibration.  Tint  in  color 
is  analogous  to  quality  in  sound,  both  being  the  result  of 
the  mixture  of  vibrations  of  different  periods.  While 
sound-waves  are  propagated  chiefly  in  the  air,  light-waves 
are  propagated  in  the  ether.  Light,  like  sound,  originates 
in  the  vibrations  of  particles  of  gross  matter ;  but  the  vi- 
brations which  originate  light  are  much  more  minute  and 
more  rapid  than  those  which  give  rise  to  sound.  The 
molecules  of  a  luminous  body  are  usually  capable  of  exe- 
cuting vibrations  of  several  periods,  and  hence  the  light 
which  they  give  out  is  seldom  homogeneous.  As  in  sound, 
so  in  light,  a  body  is  capable  of  intercepting  or  absorbing 


LIGHT.  1 89 

the  vibrations  whose  periods  are  synchronous  with  those 
of  its  own  molecules.*  Double  refraction  and  polarization 
show  that  while  in  sound  the  vibrations  are  longitudinal, 
they  are  transverse  in  light,  and  that  in  ordinary  white 
light  these  vibrations  are  executed  in  every  plane.  On 
passing  through  a  crystalline  body  these  vibrations  are 
sorted  and  arranged  in  two  sets.  When  the  vibrations 
are  all  executed  in  the  same  plane  the  ray  is  said  to  be 
polarized.  Two  rays  of  polarized  light  cannot  interfere 
so  as  to  destroy  each  other  unless  they  are  polarized  in  the 
same  plane  ;  but  they  may  interfere  so  as  to  make  the 
molecules  of  the  resultant  ray  move  in  circles  or  ellipses, 
or  so  as  to  twist  the  plane  of  polarization. 

The  rainbow  is  caused  by  the  reflection  and  refraction 
of  light  in  the  rain-drop.  The  colors  are  due  partially  to 
dispersion  and  partially  to  interference. 

An  image  of  an  object  can  be  formed  in  the  focus  of  a 
converging  lens  or  of  a  concave  mirror.  The  rays  of  light 
on  entering  the  eye  are  brought  to  a  focus  upon  the  retina 
by  means  of  the  cornea  and  crystalline  lens.  The  vibra- 
tions of  the  ether  are  taken  up  by  the  rods  and  cones, 
and  communicated  to  the  nerve-fibres,  and  thence  to  the 
brain.  The  distinctness  of  vision  increases  with  the  dis- 
tinctness, the  size,  and  the  brightness  of  the  image  upon 
the  retina ;  provided  the  illumination  is  not  too  strong,  in 
which  case  the  eye  is  blinded.  Perfect  eyes  can  adjust 
themselves  to  any  distance  from  a  few  inches  to  infinity. 
Other  eyes,  owing  to  a  defective  form  of  the  ball,  can  ad- 
just themselves  only  to  a  limited  range  of  distances,  some 
being  able  to  see  with  distinctness  only  near  objects,  and 
others  only  remote  ones.  These  defects  can  be  partially 
remedied  by  the  use  of  glasses.  As  the  eye  grows  old  it 
loses  its  power  of  adjustment. 

The  size  of  the  image  upon  the  retina  increases  as  the 
object  is  brought  nearer  to  the  eye.  The  microscope  is  an 


190  LIGHT. 

instrument  which  enables  the  eye  to  see  an  object  at  a 
very  short  distance  ;  and  the  telescope,  an  instrument 
which  enables  it  to  see  a  very  distant  object. 

The  more  refrangible  rays  of  the  spectrum  have  a  chem- 
ical action,  which  is  now  employed  in  taking  photo- 
graphic pictures. 


III. 
HEAT 


NATURE  AND  PROPAGATION  OF 
HEAT. 


RADIATION. 

177.  Heat  is  Radiated  in  all  Directions.  —  When  we  come 
near  a  stove  we  feel  its  heat,  no  matter  on  what  side  of  it 
we  may  be  ;  that  is,  the  stove  radiates  its  heat  in  all  di- 
rections. 

Again,  if  a  small  metallic  sphere  be  heated,  and  delicate 
thermometers  be  placed  on  different  sides  of  it  at  equal 
distances  from  its  centre,  they  will  all  indicate  the  same 
temperature  ;  showing  that  the  sphere  radiates  heat  equally 
well  in  every  direction. 

Radiant  heat,  like  light,  diminishes  in  intensity  as  the 
square  of  the  distance  increases,  and  for  the  same  reason. 

178.  Heat  traverses  Space  in  Straight  Lines  and  with  the 
Velocity  of  Light.  —  Heat  and  light  come  to  the  earth  .to- 
gether in  the  sun's  rays,  and  we  have  seen  that  these  move 
in  straight  lines  and  with  a  velocity  of  about  190,000  miles 
a  second. 

179.  Luminous  and  Obscure  Heat.  —  Heat  which  is  radi- 
ated  from  a  non-lurninous  source,  as  from  a  ball  heated 
below  redness,  is  called  obscure  heat ;  while  that  radiated 
from  a  luminous  source,  as  from  the  sun  or  from  a  ball 
heated  to  redness,  is  called  luminous  heat. 

1 80.  Diathermanous  Bodies.  —  Some  substances,  as  air, 
allow  radiant  heat  to  pass  readily  through  them,  and  are 

9  M 


194 


HEAT. 


called  diathermanous.  The  term  is  derived  from  the  Greek 
words  dia,  through,  and  thermos,  heat. 

If  a  plate  of  glass  be  held  up  before  an  iron  ball  heated 
to  dull  redness,  a  delicate  thermometer  held  behind  the 
plate  will  be  scarcely,  if  at  all,  affected.  If,  however,  a 
plate  of  rock  salt  be  put  in  place  of  the  glass,  the  ther- 
mometer rapidly  rises.  Glass,  then,  though  one  of  the 
most  transparent  bodies,  is  by  no  means  one  of  the  most 
diathermanous.  Rock  salt  is  the  most  diathermanous  of 
all  known  solids,  and  is  to  radiant  heat  what  glass  is  to 
light. 

1 8 1.  Heat  is  Reflected  in  the  Same  Way  as  Light.  —  That 
luminous  heat  is  reflected  in  the  same  way  as  light  is  shown 
by  the  fact  that,  when  the  sun's  rays  are  reflected  to  a  focus 
by  a  concave  mirror,  that  focus  is  the  hottest,  as  well  as 
the  brightest,  part  of  the  beam. 

At  A  (Figure  147)  in  the  focus  of  the  concave  mirror 
B  C  is  placed  a  copper  ball  heated  below  redness,  and  the 

Fig.  147- 


bulb  of  a  delicate  thermometer  is  placed  at  D  in  the  focus 
of  the  concave  mirror  E  F.  The  mercury  rises  at  once.  If 
the  thermometer  be  moved  away  from  D  in  any  direction, 
the  mercury  falls.  It  is  evident,  then,  that  the  heat-rays 
are  concentrated  at  the  focus  of  the  mirror  E  F.  Now  we 


HEAT.  195 

know  that  light-rays  diverging  from  A  would,  on  falling 
upon  the  mirror  B  C,  be  reflected  in  parallel  lines  to  the 
mirror  £  F,  and  from  this  mirror  to  its  focus  D ;  and  it  is 
clear  that  the  heat-rays  have  been  reflected  in  the  very 
same  way. 

Radiant  heat,  then,  both  luminous  and  obscure,  is  re- 
flected in  the  same  way  as  light. 

182.  Radiant  Heat  is  Refracted  in  the  Same  Way  as 
Light.  —  That  luminous  heat  is  refracted  like  light  is 
shown  by  the  fact  that  the  heat  of  the  sun's  rays  is  re- 
fracted by  a  converging  lens  to  the  same  focus  as  the  light. 
The  refraction  of  ordinary  obscure  heat  cannot  be  shown 
by  a  glass  lens,  since  it  is  not  sufficiently  diathermanous 
(180).  If,  however,  a  lens  of  rock  salt  be  held  before  a 
source  of  obscure  heat,  as  shown  in  Figure  148,  and  the 
face  of  a  thermopile  *  be  placed  at  the  focus  of  this  lens, 

Fig.  148. 


the  galvanometer  needle  at  once  turns  aside,  showing  a 
rise  of  temperature.  If  the  face  of  the  pile  be  placed 
anywhere  else  than  at  the  focus,  no  rise  of  temperature  is 
indicated. 

Fig.  149. 


Again,  if  the  rays  of  obscure  heat  be  allowed  to  fall  upon 
a  prism  of  rock  salt,  they  will  be  turned  aside,  as  shown  in 

*  For  the  thermo-electric  battery,  or  thermopile,  see  §  248,  p.  248, 
and  §  286,  p.  284. 


196 


HEAT. 


Figure  149,  in  exactly  the  same  way  as  rays  of  light  would 
be  in  passing  through  the  same  prism. 

These  experiments  show  that  radiant  heat,  whether  lu- 
minous or  obscure,  is  refracted  just  like  light. 

183.  Heat  is  Dispersed  in  the  Same  Way  as  Light.  — In 
Figure  150  we  have  a  thermopile  of  peculiar  construction. 
In  the  middle  of  the  brass  plate  A  B  is  a  narrow  vertical 
slit,  so  arranged  that  its  width  can  be  varied  at  pleasure. 
Behind  this  slit  is  the  face  of  the  thermopile,  whose  ele- 
ments are  arranged  not  in  a  cube,  as  usual,  but  in  a  single 
row.  By  means  of  the  ivory  handle  seen  at  the  bottom, 
the  brass  plate  which  serves  as  a  screen  can  be  moved 
to  and  fro  with  great  regularity  and  precision.  If  now 

this  thermopile  be  connected 
with  a  delicate  galvanometer, 
and  the  solar  spectrum  from 
an  ordinary  glass  lens  be  al- 
lowed to  fall  upon  the  screen, 
the  needle  at  once  indicates  a 
rise  of  temperature.  If  we 
move  the  face  of  the  pile 
backward  and  forward,  we 
find  that  the  heat  is  dis- 
persed throughout  the  whole 
length  of  the  spectrum,  but 
that  it  grows  more  and  more 
intense  as  we  approach  the 
red  or  least  refrangible  end  ; 
and  when  we  move  the  slit 
into  the  dark  space  beyond 
the  red,  we  are  surprised  to  find  that  the  heat  is  more 
intense  there  than  anywhere  else.  The  heat,  however, 
extends  but  a  little  way  beyond  the  red  end. 

This  experiment  shows,  (i)  that  radiant  heat  is  dis- 
persed like  light  in  passing  through  a  prism  ;  (2)  that 


HEAT.  197 

obscure  as  well  as  luminous  heat  is  radiated  from  a  lu- 
minous source  ;  and  (3)  that  obscure  heat  is  less  refrangi- 
ble than  luminous  heat. 

184.  Heat  and  Light  are  one  and  the  same.  — We  have 
now  seen  that  radiant  heat  and  light  are  reflected,  re- 
fracted, and  dispersed  in  precisely  the  same  way.  It  has 
also  been  found  by  difficult  and  delicate  experiments  that 
radiant  heat  can  also  be  polarized  in  the  same  way  as  light. 
These  facts  seem  to  lead  to  the  conclusion  that  light  and 
heat  are  the  same  thing,  and  the  following  fact  proves  this 
beyond  a  doubt. 

We  have  learned  that  the  solar  spectrum  is  crossed  by 
dark  lines,  known  as  Fraunhofer 's  lines  (112).  Now  atf 
examination  of  the  spectrum  with  a  very  delicate  ther 
mopile  has  shown  that  these  dark  lines  are  also  devoid  of 
heat,  and,  furthermore,  that  similar  dark  or  cold  lines  exist 
in  the  obscure  part  of  the  spectrum  beyond  the  red  end, 
where  the  heat  is  most  intense.  Again,  these  dark  lines 
have  been  shown  to  be  chemically  inactive,  and  similar 
inactive  lines  are  found  beyond  the  violet  end  in  the 
obscure  chemical  part  of  the  spectrum.  The  existence  of 
these  blank  lines  throughout  the  whole  length  of  the 
spectrum,  in  the  obscure  as  well  as  in  the  luminous  part, 
and  the  absence  of  both  heat  and  chemical  activity  in 
the  dark  lines  found  in  the  luminous  part,  prove  con- 
clusively that  the  thermal,  the  luminous,  and  the  chemical 
rays  are  one  and  the  same  thing. 

Passing  from  the  obscure  end  of  the  spectrum  beyond 
the  red  to  the  obscure  end  beyond  the  violet,  we  meet 
with  vibrations  of  greater  and  greater  rapidity,  but  differing 
in  nothing  else.  A  portion  of  these  vibrations  at  the  lower 
or  thermal  end  of  the  spectrum  are  able  to  affect  only 
those  nerves  which  give  us  the  sensation  of  heat ;  another 
portion,  including  the  luminous  part  of  the  spectrum,  are 
able  to  affect  these  nerves  and  at  the  same  time  the 


198  HEAT. 

nerves  of  the  eye,  and  also  to  develop  chemical  action  ; 
a  third  portion,  or  those  beyond  the  violet  end,  are  able 
only  to  cause  chemical  action.  Luminous  heat  and  light, 
then,  are  exactly  the  same  thing  ;  and  obscure  heat  differs 
from  luminous  heat  only  as  one  color  of  the  spectrum 
differs  from  another. 

If  there  is  need  of  further  proof  that  obscure  heat  differs 
from  light  only  in  the  rapidity  of  the  vibration,  it  is  fur- 
nished by  an  experiment  of  Dr.  Draper's.  He  gradually 
raised  the  temperature  of  a  platinum  wire  till  it  was  of  a 
white  heat,  and  examined  its  spectrum  throughout  the  pro- 
cess. At  first  the  spectrum  contained  only  the  obscure 
thermal  rays ;  then  the  least  refrangible  red  rays  appeared, 
followed  in  succession  by  the  orange,  yellow,  green,  blue, 
indigo,  and  violet  ;  and  after  these  came  the  obscure 
chemical  rays. 

185.  The  Proportion  of  Obscure  and  Luminous  Radiation 
in  the  Electric  Light  and  in  Sunlight.  —  Professor  Tyndail 
discovered  that  a  solution  of  iodine  in  bisulphide  of  carbon, 
which  is  so  opaque  that  a  layer  of  .07  of  an  inch  in  thick- 
ness is  sufficient  to  cut  off  all  the  light  from  the  most 
brilliant  gas-flame,  is  almost  perfectly  diathermanous  to 
obscure  heat,  even  in  very  much  thicker  layers.  A  solu- 
tion of  this  kind,  contained  in  a  narrow  cell  whose  sides 
are  polished  plates  of  rock  salt,  separates  sharply  the 
obscure  from  the  luminous  heat,  whatever  may  be  their 
source.  With  this  delicate  apparatus  he  examined  the 
obscure  heat  in  the  rays  of  the  sun  and  in  the  electric  light, 
and  found  that  it  was  far  greater  than  the  luminous  heat. 
By  giving  the  cell  the  form  of  a  prism,  he  obtained  a 
spectrum  of  this  obscure  heat.  Figure  151  shows  the 
proportion  of  the  obscure  thermal  to  the  luminous  part 
of  the  spectrum  of  the  electric  light.  The  height  of  the 
curve  shows  the  intensity  of  the  radiation  at  each  point. 
It  is  seen  that  the  luminous  rays  of  the  electric  light  are 


HEAT.  199 

insignificant  in  comparison  with  the  obscure  ones.  This 
same  thing  is  true  of  the  radiations  from  the  sun,  though 
the  disproportion  between  the  luminous  and  the  obscure 

Fig-  151- 

B 


jj 

parts  is  not  quite  so  great,  owing  probably  to  the  fact  that 
many  of  the  obscure  rays  are  absorbed  in  passing  through 
the  atmosphere. 

1 8 6.  The  Obscure  Radiation  increases  in  Intensity  with 
the   Temperature.  —  Tyndall   heated   a  spiral   of  platinum 
wire  from  dull  redness  to  full  white  heat,  and  by  means 
of  the  iodine    solution   examined   its  obscure  radiations. 
He  found  that  as  its  temperature  rose  it  not  only  gave 
off  more  and  more  refrangible  rays,  as  Draper  had  shown 
(184),  but  also  that  its  obscure  radiations  were  powerfully 
augmented.      It  had  previously  been   supposed  that  the 
effect  of  raising  the  temperature  of  a  body  was  only  to 
add  to  its  radiations  those  of  sherter  periods.     Tyndall's 
experiment,  however,  has  shown  that  the  effect  of  raising 
the  temperature  is  both  to  add  quicker  vibrations  and  to 
augment  the  intensity  of  those  which  already  exist. 

The  hotter  a  body,  then,  the  more  powerful  its  obscure 
radiations. 

187.  Invisible  Foci. — By  means  of  the  opaque  iodine 
solution,  Tyndall  was  able  to  show  effects  of  obscure  heat 
far  more  striking  than  had  ever  been  shown  before,  for  he 
could  use  the  obscure  radiations   from  the  most  intense 


200  HEAT. 

sources  of  heat.  He  placed  a  concave  mirror  behind  the 
carbon  points  in  the  electric  lamp,  and  converged  its  pow^ 
erful  beam  to  a  focus  a  short  distance  in  front.  In  this 
focus  there  was,  of  course,  formed  a  very  bright  luminous 
image  of  the  carbon  points.  He  then  cut  off  all  the  lumi- 
nous rays  with  an  iodine  cell.  The  image  disappeared  from 
sight,  but  an  invisible  "  thermograph "  remained.  It  is 
only  the  peculiar  structure  of  our  eyes  which  prevents  our 
seeing  such  a  picture.  Place  a  piece  of  white  paper  at  the 
focus  of  the  mirror,  and  the  image  chars  itself  out.  If 
black  paper  is  used,  two  holes  are  burned  in  it,,  corre- 
sponding to  the  images  of  the  two  carbon  points.  If  a 
thin  piece  of  carbon  in  a  vacuum  be  placed  at  the  focus, 
the  radiant  heat  is  converted  into  light,  and  the  latent 
image  becomes  visible.  A  thin  sheet  of  platinized  plati- 
num will  bring  out  the  image  even  in  the  air.  The  intense 
heat  at  this  invisible  focus  may  be  shown  by  many  other 
experiments,  as  the  melting  of  lead,  the  burning  of  zinc 
and  magnesium,  and  the  like. 

Similar  experiments  may  be  tried  by  bringing  the  lumi- 
nous rays  to  a  focus  by  a  rock-salt  lens,  and  interposing  an 
iodine  cell,  or,  what  is  better,  a  hollow  lens  of  rock  salt 
filled  with  the  iodine.  Sunlight  produces  similar  effects, 
and  in  using  it  a  glass  lens  may  be  substituted  for  a  rock- 
salt  one,  though  with  less  brilliant  results. 

188.  Calorescence  and.  Fluorescence.  —  In  the  above  ex- 
periment of  Tyndall's,  the  platinum  foil  cannot  have  be- 
come hotter  than  the  focus  itself,  yet  it  became  luminous 
while  the  focus  was  obscure.  Again,  when  a  cylinder  of 
lime  is  put  in  the  oxy-hydrogen  flame,  its  temperature  can- 
not be  higher  than  that  of  the  flame,  yet  it  becomes 
intensely  luminous.  Platinum,  then,  and  other  solids 
have  the  power  of  raising  the  refrangibility  of  the  obscure 
rays  so  as  to  render  them  luminous.  This  change  of  re- 
frangibility is  called  calorescence. 


HEAT.  201 

On  looking  through  a  prism  at  the  incandescent  image 
of  the  carbon  points  on  the  platinum  foil,  Tyndall  found 
that  the  light  from  it  gave  a  complete  spectrum,  showing 
that  the  obscure  rays  had  been  converted  by  the  platinum 
into  red,  orange,  yellow,  green,  blue,  and  even  violet. 

When  the  ordinary  spectrum  is  allowed  to  fall  on  a 
screen  washed  over  with  a  solution  of  the  sulphate  of 
quinine,  the  ultra-violet  rays  become  luminous,  showing 
that  their  refrangibility  has  been  lowered.  This  phe- 
nomenon, which  is  just  the  opposite  of  calorescence,  is 
called  fluorescence. 

Phosphorescence,  that  is,  the  property  which  certain 
bodies  have  of  shining  in  the  dark  after  they  have  been 
exposed  to  the  light,  is  probably  nothing  but  a  persistent 
form  of  fluorescence. 

SUMMARY. 

Heat  is  radiated  from  its  source  in  all  directions.     (177.) 

It  traverses  space  in  straight  lines  with  the  velocity  of 
light.  (178.) 

Radiated  heat  may  be  luminous  or  obscure.     (179.) 

Bodies  which  allow  heat  to  pass  readily  through  them 
are  called  diathermanous.  (180.) 

Radiant  heat  is  reflected,  refracted, .  and  dispersed  in 
the  same  way  as  light. 

Obscure  heat  is  less  refrangible  than  luminous  heat. 
(181-183.) 

Heat  and  light  are  the  same  thing. 

The  different  kinds  of  heat  differ  only  in  the  rapidity  of 
the  vibrations  in  which  they  originate  and  are  propagated. 

(i84.) 

The  obscure  radiations  of  the  electric  lamp  and  the  sun 
are  much  more  abundant  than  the  luminous  radiations. 

(185-) 

9* 


202  HEAT. 

The  obscure  radiations  increase  in  intensity  as  the  tem- 
perature of  the  body  rises.  (186.) 

Invisible  foci    may  be    formed   by  obscure   radiations. 

(i87.) 

The  refrangibility  of  the  obscure  thermal  radiations  may 
be  raised  so  that  they  will  become  luminous ;  while  that 
of  the  obscure  chemical  radiations  may  be  lowered.  The 
former  change  of  refrangibility  is  called  calorescence ;  the 
latter,  fluorescence.  (188.) 

ABSORPTION. 

189.  Different  Solids  and  Liquids  absorb  the  Same  Kind  of 
Heat  with  Different  Degrees  of  Readiness.  —  In  Figure  152 
M  is  a  perforated  screen,  B  is  a  copper  ball  heated  to 
dull  redness,  and  T  is  a  thermopile.  A  plate  of  glass 
is  put  upon  the  shelf  at  S  behind  the  screen.  Few  rays 

Fig.  15*. 


of  heat  reach  the  pile.  If  a  plate  of  rock  salt  of  the 
same  thickness  be  substituted  for  the  glass,  abundance 
of  heat  reaches  the  pile.  The  diathermancy  of  liquids 
can  be  found  in  the  same  way,  by  enclosing  them  in  a 
glass,  or,  better,  a  rock-salt  cell,  which  is  placed  upon 
the  shelf.  It  is  found  in  this  way  that  different  solids 
and  liquids  absorb  the  same  kind  of  heat  very  differently. 


HEAT. 


190.  The  Same  Solid  or  Liquid  absorbs  Heat  of  Different 
Kinds  in  Different  Proportions.  —  By  using  different  sources 
of  heat,  such  as  a  Locatelli  lamp,  copper  of  different  tem- 
peratures, and  incandescent  platinum,  it  is  found  that  the 
same  solid  or  liquid  absorbs  heat  from  these  sources  in 
very  different  proportions. 

In  this  way  Melloni  constructed  the  following  Table,  in 
which  the  heat  from  each  source  transmitted  by  each 
substance  is  compared  with  that  from  the  same  source 
transmitted  by  the  air,  the  latter  being  called  100  :  — 


Names  of  substances  reduced 
to  a  common  thickness  of  .1 
of  an  inch  (2.6  millim.). 

Transmissions  :  percentage  of  the 
total  radiation. 

Locatelli 
Lamp. 

Incan- 
descent 
Platinum. 

Copper  at 
400°  C. 

Copper  at 
1  00°  C. 

I  Rock  salt  

92.3 
74.0 
72.0 

54-0 
39-o 
39-o 
38.0 
37-o 
34-o 
330 
32.0 
24.0 
23.0 

2I.O 
21.0 

1  8.0 
1  8.0 
1  8.0 
14.0 

II.O 
II.O 
II.O 

9.0 
8.0 
6.0 

92-3 

77.0 
69.0 

28.0 
24.0 
28.0 
28.0 
28.0 
24.0 
23.0 

1  8.0 
19.0 
9.0 

5-o 

12.0 

16.0 

3-o 
5-0 

2.0 

3-o 
5-0 

2.0 
1.0 

o-5 

92.3 
oo.o 

42.0 

6.0 
6.0 
6.0 
6.0 
15.0 
4.0 
4.0 

3-o 
6.0 

2.0 
0.0 

8.0 
3-o 

0.0 
0.0 

o.o 
o.o 

0.0 
0.0 
0.0 

o.o 

92.3 

54-o 
33-o 

O.O 

o.o 

0.0 

3-3 
3-o 
o.o 
o.o 
o.o 

0.0 
0.0 
0.0 

o.o 

0.0 
0.0 
0.0 

o.o 

0.0 
0.0 
0.0 

o.o 
o.o 

0.0 

2  Sicilian  sulphur  

3  Fluor  spar 

A  Bervl 

5  Iceland  spar  

6  Glass  

7  Rock  crystal  (clear) 

8  Smoky  quartz  , 

9  Chromate  of  potash  

10  \Vhite  topaz 

II  Carbonate  of  lead  

12  Sulphate  of  baryta.    .  .  . 

13  Felspar  .  . 

14  Amethyst  (violet) 

15  Artificial  amber  

1  6  Borate  of  soda  

17  Tourmaline  (deep  green)  .  .  . 
1  8  Common  gum. 

19  Selenite  

20  Citric  acid  

21  Tartrate  of  potash  
22  Natural  amber 

27  Alum 

24  Sugar  candy  

25  Ice  

The  following  Table  gives  the  per  cent  of  total  radiation 
transmitted  by  different  liquids  :  — 


404  HEAT. 


Name,  of  Liquid, 
Bisulphide  of  carbon  ..........................  63 

Bichloride  of  sulphur  .........................  63 

Protochloride  of  phosphorus  ...................  62 

Essence  of  turpentine  ........................  31 

Olive  oil  ....................................  30 

Naphtha  ....................................  28 

Essence  of  lavender  ..........................  26 

Sulphuric  ether  ..............................  21 

Sulphuric  acid  ...............................  17 

Hydrate  of  ammonia  ..........................  15 

Nitric  acid  ..................................  15 

Absolute  alcohol  .............................  15 

Hydrate  of  potash  ............................  13 

Acetic  acid  ..................................  ia 

Pyroligneous  acid  ............................  12 

Concentrated  solution  of  sugar  ................  12 

Solution  of  rock  salt:  .  ........................  12 

White  of  egg  ................................  1  1 

Distilled  water  ...............................  1  1 


191.  Quality  of  Heat.  —  If  the  rays  which  have  passed 
through  a  plate  of  any  substance  be  allowed  to  fall  upon 
a  second  plate  of  the  same,  they  are  transmitted  in  much 
larger  proportion  than  at  first.  The  rays  which  fall  upon 
the  first  plate  are  sifted,  and  those  which  cannot  pass 
through  that  substance  are  absorbed.  When,  therefore, 
the  rays  fall  upon  the  second  plate,  they  are  nearly  all 
transmitted. 

From  the  fact  that  the  heat  radiated  from  different 
sources  is  absorbed  differently  by  the  same  substance, 
it  is  said  to  be  of  different  quality.  In  no  case  is  the 
heat  homogeneous,  and  in  the  heat  radiated  from  different 
sources  vibrations  of  different  periods  are  differently  mixed. 
It  is  these  different  mixtures  of  vibrations  of  different 
periods  that  give  to  the  heat  from  each  source  its  peculiar 
quality  ;  as  the  mixture  of  rays  of  different  periods  gives 
to  the  light  from  different  bodies  its  peculiar  tint. 


HEAT.  205 

192.  Different  Gases  absorb  the  Same  Quality  of  Heat  in 
Different  Proportions.  —  In  Figure  153,  A  is  a  copper  box, 
against  one  face  of  which  a  steady  gas-flame  is  made  to 
play.  G  is  a  chimney,  and  B  is  an  air-chamber,  beyond 
which  is  a  long  glass  tube,  both  ends  of  which  are  closed 
with  rock-salt  plates.  The  pipe  D  connects  this  chamber 
with  an  air-pump.  The  chamber  is  surrounded  with  a 
collar  through  which  water  is  kept  flowing,  in  order  that 

Fig.  153- 


the  walls  may  not  become  heated.  The  heat  radiated 
from  the  copper  box  passes  first  through  this  chamber  and 
then  through  the  tube  beyond.  The  tube  is  first  filled 
with  carefully  dried  air,  and  the  deflection  of  the  galva- 
nometer needle  is  noted.  The  tube  is  next  filled  with 
carefully  dried  olefiant  gas  ;  and  it  is  found  that  only  about 
.001  as  much  heat  is  radiated  through  the  tube  as  at  first. 
This  shows  that  different  gases  absorb  the  same  quality  of 
heat  very  differently. 


206  HEAT. 

The  following  table  is  taken  from  Tyndall  :  — 

Absorption  under 

Name  of  Gas.  a  pressure  of  one 

atmosphere. 

Air i 

Oxygen I 

Nitrogen I 

Hydrogen I 

Chlorine 39 

Hydrochloric  acid 62 

Carbonic  oxide 90 

Carbonic  acid 90 

Nitrous  oxide 355 

Sulphide  of  hydrogen 390 

Marsh  gas 403 

Sulphurous  acid 710 

defiant  gas 970 

Ammonia 1 195 

If,  instead  of  comparing  the  gases  at  the  common  pres- 
sure of  one  atmosphere,  or  30  inches,  we  compare  them 
at  the  common  pressure  of  one  inch,  we  shall  find  their 
absorptive  power  differing  in  even  a  more  striking  man- 
ner, as  is  shown  in  the  following  table  from  Tyndall  :  — 

Absorption 

Name  of  Gas.  under  i  inch 

pressure. 

Air i 

Oxygen I 

Nitrogen i 

Hydrogen i 

Chlorine 60 

Bromine 160 

Carbonic  oxide 750 

Hydrobromic  acL' 1005 

Nitric  oxide i  ~jQ 

Nitrous  oxide 1 860 

Sulphide  of  hydrogen 2100 

Ammonia 7260 

Olefiant  gas 7950 

Sulphurous  acid 8800 

"What   extraordinary    differences,"   Tyndall  adds,    "in 


HEAT. 


207 


Fig-  154- 


the  constitution  and  character  of  the  ultimate  particles 
of  various  gases  do  the  above  results  reveal !  For  every 
individual  ray  struck  down  by  the  air,  oxygen,  hydrogen, 
or  nitrogen,  the  ammonia  strikes  down  a  brigade  of  7,260 
rays  ;  the  olefiant  gas,  a  brigade  of  7,950  ;  while  the  sul- 
phurous acid  destroys  8,800." 

193.  The  Same  Gas  absorbs  Different  Qualities  of  Heat  in 
Different  Proportions.  —  In  Figure  154  we  have  what  is 
called  a  platinum  lamp,  s  is  a  spiral  of  platinum  wire 
within  a  glass  globe  ;  d  is  an  open- 
ing in  the  side  of  the  globe  through 
which  the  heat  from  the  spiral  is 
radiated  ;  a  is  a  concave  mirror  for 
collecting  and  condensing  the  heat. 
The  platinum  spiral  is  connected  with 
a  galvanic  battery,  and  by  regulating 
the  strength  of  the  current  we  can 
heat  the  wire  to  any  desired  tem- 
perature. By  using  this  lamp  as  a 
source  of  heat,  Tyndall  showed  that  the  same  gas  or  vapor 
absorbs  different  qualities  of  heat  very  differently.  Some 
of  the  results  of  his  experiments  are  given  in  the  following 
Table:  — 


Name  of  Vapor. 

Source  of  heat  :  platinum  spiral. 

Barely 

visible. 

Bright- 
red. 

White- 
hot. 

Near 
fusion. 

Bisulphide  of  carbon  

6.5 
9.1 
12.5 
21.3 
26.4 

35-8 
43-4 
46.2 
49.6 

II 

9.6 

17.7 
20.6 

27-5 

3M 

31-9 
34-6 

2.9 
5.6 

7-8 

12.8 

16.5 

22.7 
25-9 
25.1 
27.2 

2-5 

3-9 

23-7 
21.3 

Chloroform           

Iodide  of  methyl.                  .... 

"       "  ethvl 

Benzole 

Amylene  

Sulphuric  ether  

Formic          "      

Acetic           "                       ... 

208  HEAT. 

The  gradual  increase  of  penetrative  power  as  the  tem- 
perature rises  is  here  very  manifest.  By  raising  the  tem- 
perature of  the  spiral  from  a  barely  visible  to  an  intensely 
white  heat,  we  reduce  the  absorption  in  the  case  of  bisul- 
phide of  carbon  and  chloroform  to  less  than  one  half. 

194.  Vapors  absorb  the  Sam?  Quality  of  Heat  in  the  Same 
Order  as  their  Liquids.  —  Tyndall  has  arranged  the  follow- 
ing liquids  and  their  vapors  in  the  order  in  which  he  found 
them  to  absorb  the   same   quality  of  heat,  the  quantity 
of  vapor  used   in   each  case  being  proportional   to  that 
of  the  liquid  :  — 

Liquids.  Vapors. 

Bisulphide  of  carbon,  Bisulphide  of  carbon, 

Chloroform,  Chloroform, 

Iodide  of  methyl,  Iodide  of  methyl, 

"      "  ethyl,  "       "  ethyl, 

Amylene,  Amylene, 

Sulphuric  ether,  Sulphuric  ether, 

Acetic,          "  Acetic  " 

Formic,         "  Formic          " 

Alcohol,  Alcohol, 

Water,  Water.* 

We  see  from  this  table  that  the  order  of  absorption  in 
vapors  and  their  liquids  is  the  same.  When  the  molecules 
are  freed  from  the  bonds  which  hold  them  in  the  liquid 
state,  they  do  not  change  their  absorptive  power. 

195.  Good  Absorbers  are  Good  Radiators.  —  Coat  all  the 
sides  of  a  tin  box  except  one  with  a  varnish  or  lamp-black, 
fill  it  with  boiling  water,  and  expose  each  side  in  turn  to 
the  face  of  a  thermopile.     It  will  be  found  that  the  heat  is 
radiated  slowly  from  the  metallic  surface  as  compared  with 
the  coated  surfaces. 

*  Aqueous  vapor,  when  unmixed  with  air,  condenses  so  readily 
that  it  cannot  be  directly  examined  in  the  experimental  tube. 


2OQ 


In  Figure  155  we  have  Fig.  155. 

a  plate  of  tin  m  n  uncoat- 
ed,  and  another  op  coat- 
ed with  lamp-black.  The 
plates  are  connected  by 
a  wire  at  the  top,  and  to 
the  back  of  each  is  sold- 
ered a  little  bar  of  bis- 
muth. These  bars  are 
connected  with  a  delicate 
galvanometer.  If  we  heat 
the  junction  of  one  of 
these  bars  with  the  plate 
by  putting  the  finger  upon  it,  the  galvanometer  shows  that 
the  current  is  flowing  in  one  direction  ;  if  we  allow  this  to 
cool  and  heat  the  other  in  the  same  way,  the  galvanometer 
shows  a  current  flowing  in  the  opposite  direction  ;  if  we 
heat  them  both  equally  at  the  same  time,  no  current  is 
indicated.  A  heated  copper  ball  is  now  placed  just  half- 
way between  the  two  plates,  so  as  to  radiate  heat  equally 
to  each.  The  needle  at  once  shows  a  current  flowing  from 
the  plate  op,  which  must  therefore  have  become  more 
heated  than  m  n.  The  coated  plate,  which  was  the  best 
radiator,  is,  therefore,  the  best  absorber. 

In  Figure  156  fis  a  thermopile  connected  with  a  gal- 
vanometer ;  C,  a  heated  copper  ball  placed  above  a  tube 
A.  The  direct  radiation  of  the  ball  is  cut  off  from  the 
pile  by  means  of  the  screen  S.  L  is  a  cube  filled  with  hot 
water  and  placed  at  such  a  distance  from  the  pile  as  to 
warm  the  face  towards  it  just  as  much  as  the  opposite  face 
is  warmed  by  the  current  of  air  streaming  up  over  the  hot 
ball.  Different  gases  are  now  forced  through  the  tube 
against  the  ball,  by  which  they  are  heated.  On  rising 
above  the  screen,  they  radiate  their  heat  to  the  pile.  If 
they  radiate  just  as  much  heat  as  the  air,  the  needle  will 

N 


210 


not  move  ;  if  they  radiate  more  heat  than  the  air,  it  will 
move  in  such  a  way  as  to  show  that  the  left  face  of 
the  pile  is  heated  more  than  the  other ;  if  less  than  the 
air,  it  will  move  in  the  opposite  direction.  By  noticing 
how  much  the  needle  turns  in  each  case,  we  can  compare 
the  radiating  power  of  the  different  gases  used.  In  this 
way  it  is  found  that  those  gases  which  are  the  best  ab- 
sorbers are  also  the  best  radiators. 

196.  The  Molecules  of  a  Substance  radiate  Heat  by  Com- 
municating their  Motion  to  the  Ether,  and  absorb  Heat  by 
Taking  up  Motion  from  the  Ether.  —  In  the  study  of  light 
we  have  learned  that  the  molecules  of  substances  are  im- 
mersed in  the  all-pervading  ether,  and  that  the  molecules 
of  each  substance  are  capable  of  vibrating  in  certain  defi- 
nite periods.  When  the  ethereal  vibrations  dash  against 
the  molecules  of  a  body,  these  molecules  will  take  up  the 
vibrations  which  are  synchronous  with  their  own,  and  allow 
the  others  to  pass  on.  The  former  vibrations  are  said  to 
be  absorbed,  the  latter  transmitted.  Diathermancy,  then, 
is  synonymous  with  discord;  and  adiathermancy  (the 
opposite  of  diathermancy)  with  concord.  Hence  arises 
the  power  of  bodies  to  sift  the  vibrations  which  fall  upon 
them.  The  molecules  select  and  absorb  the  vibrations 


HEAT.  211 

which  are  synchronous  with  their  own,  and  allow  the 
others  to  pass. 

When,  on  the  other  hand,  bodies  radiate  heat,  they  im- 
part some  of  their  motion  to  the  ether  which  surrounds 
them.  Bodies  can  radiate  only  those  vibrations  which 
their  own  molecules  can  perform.  Hence  different  bodies 
radiate  different  qualities  of  heat.  That  bodies  radiate 
the  same  kind  of  heat  as  that  which  they  absorb  is  shown 
by  the  fact  that  they  are  nearly  opaque  to  their  own  radia- 
tions. Even  rock  salt,  which  is  so  diathermanous,  is  near- 
ly opaque  to  the  vibrations  given  out  by  heated  salt. 

197.  The  Absorptive  Power  of  a  Body  depends  upon 
its  Molecular  Constitution.  —  An  examination  of  the  pre- 
ceding tables  will  show  that  elementary  bodies,  such  as 
the  metals,  oxygen,  and  nitrogen,  are  poor  absorbers,  while 
compound  bodies,  such  as  olefiant  gas,  sulphurous  acid, 
and  ammonia,  are  good  ones.  This  is  as  we  should  ex- 
pect, since  the  more  complex  a  molecule  becomes  by  the 
combination  of  different  atoms,  the  more  likely  it  will  be 
to  intercept  the  vibrations  of  the  ether  in  which  it  is  im- 
mersed. The  great  absorptive  power  of  lamp-black,  one 
of  the  forms  of  carbon,  would  seem  to  be  at  variance  with 
this  view.  Lamp-black,  however,  is  not  pure  charcoal, 
but  contains  various  compounds  of  carbon  and  hydrogen  ; 
while  charcoal  itself  is  an  allotropic  state  of  carbon.  And 
the  most  probable  explanation  of  allotropic  states  is  that 
the  atoms  are  differently  grouped  into  molecules.  While 
oxygen  is  almost  perfectly  transparent  to  heat,  ozone,  an 
allotropic  state  of  oxygen,  is  quite  a  good  absorber.  This 
is  probably  due  to  the  fact  that  in  the  charcoal  and  ozone 
the  atoms  are  grouped  in  such  a  way  as  to  form  complex 
molecules. 

The  power  of  bodies  to  absorb  vibrations  from  the 
ether  is  likely  to  throw  much  light  on  their  molecular 
constitution. 


212  HEAT. 

198.  The  Molecules  of  all  Bodies  are  in  Motion.  —  It 
would  seem,  then,  that  all  the  molecules  of  gross  matter 
are  in  constant  vibration  ;  and  that,  when  acted  upon  by 
heat  or  other  force,  these  molecules  are  made  to  perform 
their  fundamental  vibrations  with  greater  energy,  and  to 
add  to  these  higher  and  higher  harmonics.  Our  organs 
of  sense  are  instruments  for  intercepting  these  vibrations 
and  transmitting  them  to  the  brain,  where  they  tell  us  all 
that  we  know  of  the  external  world.  The  eye  seems  to 
have  been  especially  formed  to  give  us  a  glimpse  of  the 
beauty  of  these  vibrations. 

SUMMARY. 

Different  qualities  of  heat  result  from  different  mixtures 
of  vibrations  of  different  periods.  (191.) 

The  same  solid,  liquid,  or  gas  absorbs  different  qualities 
of  heat  in  different  proportions  ;  while  different  solids, 
liquids,  or  gases  absorb  the  same  quality  of  heat  in  differ- 
ent proportions.  (189-193.) 

Vapors  absorb  the  same  qualities  of  heat  in  the  same 
order  as  their  liquids.  Water  is  the  best  absorber  among 
liquids,  and  watery  vapor  among  gases.  (194.) 

Good  absorbers  are  good  radiators.     (195.) 

The  molecules  of  a  substance  radiate  heat  by  communi- 
cating their  vibrations  to  the  ether,  and  absorb  heat  by 
taking  up  vibrations  from  the  ether.  (196.) 

The  absorptive  power  of  a  body  depends  on  its  molec- 
ular constitution.  (197.) 

The  molecules  of  all  bodies  seem  to  be  in  vibration  ; 
and  when  they  are  heated  their  original  vibrations  are  ren- 
dered more  intense,  and  more  rapid  vibrations  are  added 


HEAT. 


2I3 


EFFECTS  OF  HEAT  ON  BODIES. 
CONDUCTION. 

199.  The  Molecules  of  a  Body  communicate  their  Vibrations 
to  one  another.  —  We  have  now  seen  that  on  absorbing  heat 
the  molecules  of  a  body  are  made  to  vibrate  with  greater 
energy  and  in  quicker  periods.     When  one  end  of  a  poker 
is  placed  in  the  fire,  it  soon  becomes  red  hot,  and  the 
heat   slowly  travels   from   this   end   to   the  other.      This 
heat  cannot  have  been  radiated,  since  radiant  heat  travels 
at  the  rate  of  190,000  miles  a  second.     The  molecules  of 
a  solid  are  then  able  to  communicate  their  vibrations  to 
one  another  as  well  as  to  the  ether. 

This  transmission  of  heat  from  molecule  to  molecule  of 
gross  matter  is  called  conduction. 

200.  Different  Solids  conduct  Heat  differently.  —  If  several 
thermometer  bulbs  be  inserted  in  a  metallic  rod,  as  shown 

Fig.  157- 


in  Figure  157,  and  one  end  of  the  bar  be  heated,  the 
mercury  will  begin  to  rise  in  the  thermometer  nearest  the 
heated  end,  and  then  in  the  others  successively  ;  but  no 


214 


HEAT. 


amount  of  heating  will  make  the  mercury  rise  as  high  in 
the  last  thermometer  as  in  the  first.  If  now  rods  of  other 
metals  of  the  same  length  and  thickness  are  tried  in  the 
same  way,  it  will  be  found  that  the  difference  of  tempera- 
ture at  the  ends  of  the  rods  is  not  always  the  same.  The 
less  the  difference  of  temperature,  the  better  the  body 
conducts  heat. 

The  following  Table  of  conductivity  is  from  Tyndall :  — 


Name  of  Substance. 

Conductivity. 

For  Electricity. 

For  Heat. 

Silver  

IOO 

73 
59 

22 
23 
13 
II 
IO 

6 

2 

IOO 
74 

53 

24 
15 

12 

6 

2 

Copper  
Gold  
Brass 

Tin  

Iron 

Lead 

Platinum  

German  silver. 
Bismuth  

It  will  be  seen  that  the  metals  differ  widely  in  con- 
ductive power,  and  that  those  which  are  good  conductors 
of  heat  are  also  good  conductors  of  electricity. 

20 1.  Liquids  and  Gases  are  Poor  Conductors  of  Heat.  — 
In  Figure  158  a  differential  thermometer  (that  is,  a  ther- 
mometer for  finding  the  difference  of  temperature  at  two 
points)  is  placed  in  a  glass  vessel 
filled  with  water.  Heat  is  applied 
to  the  surface  of  the  water  by  means 
of  a  dish  of  heated  oil.  If  the 
water  conducted  the  heat,  the  upper 
bulb  of  the  thermometer  would  be- 
come heated  sooner  than  the  lower 
one,  and  the  thermometer  would  at 
once  indicate  a  difference  of  tem- 
perature between  the  two  bulbs. 
But  the  thermometer  is  scarcely 
affected. 


HEAT.  215 

This  experiment  shows  that  water  is  a  poor  conductor 
of  heat.  The  same  is  true  of  other  liquids,  and  even  more 
so  of  gases. 

SUMMARY.  " 

The    molecules   of   a   heated   solid   communicate   their 
vibrations  to  one  another  as  well  as  to  the  ether.     Heat 
thus  communicated  is  said  to  be  conducted.     (199.) 
Some  solids  conduct  heat  better  than  others.     (200.) 
Liquids  and  gases  are  poor  conductors.     (201.) 

TEMPERATURE. 

202.  Heat  raises  the  Temperature  of  a  Body. —  The  most 
obvious  effect  of  the  heat  absorbed  by  a  body  is  a  rise 
of  temperature.     This  rise  of  temperature  is  indicated  by 
the  sense  of  touch,  but  more  accurately  by  a  thermometer. 

203.  A  Body  in  cooling  i°  gives  out  just  as  much  Heat  as 
it  takes  to  heat  it  i°.  —  Boil  a  quarter  of  a  pound  of  water 
in  a  beaker,  and  plunge  the  bulb  of  a  thermometer  into  it, 
and  it  will  indicate  a  temperature  of  212°.     Remove  the 
beaker  from  the  source  of  heat,  and  add  a  quarter  of  a 
pound  of  water  of  a  temperature  of  70°.     Stir  the  mixture 
a  short  time  with  the  bulb  of  a  delicate  thermometer,  and 
the   temperature   will   be   found    to   be    141°.      The  first 
quarter  of  a  pound  of  water  has  then   lost  71°  and  the 
second  has  gained  71°  ;  in  other  words,  the  first  in  cooling 
i°  has  given  out  just  heat  enough  to  warm  the  second  i°. 
The  same  is  true  of  all  other  bodies. 

204.  It  requires  Different  Ainounts  of  Heat  to  raise  the 
Temperature  of  the  Same  Weight  of  Different  Bodies  i°.  —  If 
a  piece  of  tin  be  heated  to  212°  by  plunging  it  into  boiling 
water,   and  it  then   be   plunged   into  its   own  weight  of 
water  at  70°,  the  resulting  temperature  will  be  considerably 
below  141°  ;  showing  that  tin  in  cooling  i°  does  not  give 


2l6  HEAT. 

out  heat  enough  to  raise  the  water  i°.  But  the  tin  in 
cooling  i°  gives  out  just  as  much  heat  as  it  takes  to  raise 
its  temperature  i°.  Hence  it  takes  more  heat  to  raise  the 
temperature  of  a  pound  of  water  i°  than  to  raise  that  of  a 
pound  of  tin  i°.  If  copper  be  used  instead  of  tin,  the 
resulting  temperature  will  be  higher,  but  still  below  141°. 
It  requires,  then,  less  heat  to  raise  the  temperature  of  a 
pound  of  copper  i°  than  to  raise  that  of  a  pound  of  water 
i°,  but  more  than  it  takes  to  raise  that  of  a  pound  of  tin  i°. 
In  this  way  it  is  found  that  it  takes  very  different 
amounts  of  heat  to  raise  the  temperature  of  the  same 
weight  of  different  substances  i°. 

205.  Unit  of  Heat. — The   thermometer   indicates   the 
rise  of  temperature  in  a  body,  but  tells  us  nothing  of  the 
amount  of  heat  required  to  raise  the  temperature.     It  is 
therefore  desirable  to  have  some  unit  by  which  the  heat 
received  by  a  body  may  be  expressed.     The  unit  usually 
taken  is  the  amount  of  heat  required  to  raise  the  tempera- 
ture of  a  pound  of  water  i°.     A  unit  of  heat,  then,  is  the 
amount  of  heat  required  to  raise  the  temperature  of  one  potind 
of  water  i°. 

206.  Specific  Heat.  —  The   amount  of  heat  required   to 
raise  the  temperature  of  a  pound  of  any  substance  i°,  ex- 
pressed in  units,  is  called  the  specific  heat  of  that  substance. 
Thus  it  requires  ^  of  a  unit  of  heat  to  raise  the  tempera- 
ture of  one  pound  of  mercury  i°  ;  and  the  specific  heat  of 
mercury  is  therefore  ^  or  .033. 

When  we  know  the  specific  heat  of  a  body  and  also  its 
weight,  we  can  readily  find  how  many  units  of  heat  it  will 
take  to  raise  its  temperature  any  number  of  degrees. 
For  instance,  10  pounds  of  iron  have  been  raised  100°  in 
temperature,  and  the  specific  heat  of  iron  is  .1138.  To 
raise  10  pounds  of  iron  i°  in  temperature  would,  then, 
require  1.138  units  of  heat.  To  raise  it  100°,  would 
require  113.8  units  of  heat. 


HEAT.  217 

207.  The  Method  of  finding  Specific  Heat  by  Mixture. — 
One  of  the  readiest  ways  of  finding  the  specific  heat  of  a 
body  is  by  the   method  of  mixture^   as  it  is  called.     The 
substance  is  first  weighed,  then  heated  to  a  certain  tem- 
perature,  and   plunged   into  a  vessel  of  water,  and   the 
resulting  temperature  is  noted.     The  weight  of  water  and 
its  temperature  at  the  beginning  of  the  experiment  are 
supposed  to  be  known.     We  then  can  find  the  number 
of  units  of  heat  which  the  water  has  received,  and  which 
of  course  have  been  lost  by  the  heated  substance.     We  also 
know  the  number  of  degrees  the   substance  has  cooled, 
and  can  therefore  find  how  many  units  of  heat  one  pound 
of  it  would  give  out  in  cooling  i°.     Now  this  is  the  amount 
of  heat  which  it  would  take  to  raise  the  temperature  of 
one  pound  of  it  i°,  or  its  specific  heat. 

This  method  is  simple,  and  would  be  satisfactory,  were 
not  the  water  losing  heat  by  radiation  during  the  experi- 
ment. We  can,  by  trial,  find  very  nearly  the  rate  at  which 
the  water  is  radiating  its  heat,  and  thus  calculate  the  loss. 

208.  The  Method  of  finding  Specific  Heat  by  Melting.  — 
Another  method    of  finding   specific   heat  is  by  melting 
ice.      The  substance  is  first  weighed,   then  heated  to  a 
certain  temperature,  as  100°,  and  placed  in  the  vessel  M 
(Figure  159).     This  vessel  is  placed  within  the  vessel  A, 
the  space  between  the   two   being  filled   with   ice.      The 
vessel  A   is  placed  in  another,  B,  from  which  it  is  also 
separated  by  ice.     Since  the  vessel  A  is  surrounded  by 
ice,   the   heat  which   melts  the  ice  within   it  must  come 
wholly  from  the  vessel  M.     As  the  ice  in  A  melts,  the 
water   runs  off  through  the   pipe  D.     It   is   necessary  to 
know  how  much  ice  will  be  melted  by  one  pound  of  water 
cooling  i°,  or  by  one  unit  of  heat.     We  need,  then,  only 
know  how  much  ice  is  melted  by  any  substance  within  the 
box  Mt  in  order  to  find  how  many  units  of  heat  it  has 
given  up.     Dividing  this  by  the  weight  of  the  substance 

10 


218 


HEAT. 


and  by  the  number  of  degrees  it  has  cooled,  we  get  its 
specific  heat. 

Fig.  159- 


Thus,  suppose  ten  pounds  of  iron  heated  to  132°  be 
placed  in  Jlft  and  allowed  to  cool  100°,  and  that  it  is  found 
to  give  out  109  units  of  heat.  109  -j-  10  —  10.9,  which  is 
the  number  of  units  of  heat  which  would  be  given  out  by 
one  pound  cooling  100°  ;  and  10.9  -f-  ioo  =  .  109,  which 
is  the  number  of  units  one  pound  would  give  out  in  cool- 
ing i°,  or  the  specific  heat  of  iron. 

The  specific  heat  of  solids  can  be  found  by  either  of  the 
above  methods.  The  specific  heat  of  a  few  substances  is 
given  in  the  following  table  :  — 


Substance. 

Mean  Specific  Heat. 

Between  32°  and  212°. 

Between  32°  and  572°. 

Iron  

0.1098 
0.0330 
0.0927 
0.0507 
0-0557 
0.0949 
0.0355 
0.1770 

0.1218 

0.0350 
O.IOI5 
0.0549 

0.0611 
0.1013 
0-0355 
0.1990 

Mercury  

Zinc 

Antimony 

Silver 

Copper.  . 

Platinum  

Glass  

HEAT. 


2I9 


It  will  be  seen  from  this  table  that  the  specific  heat  of  a 
solid  increases  with  the  temperature.  It  will  be  noticed 
that  the  specific  heat  of  solids  is  low  compared  with  that 
of  water,  which  is  of  course  i.oo. 

209.  Specific  Heat  of  Liquids.  —  Regnault  has  found  the 
specific  heat  of  a  number  of  liquids  by  the  following 
method.  The  liquid  to  be  tried  is  put  in  the  vessel  O 
(Figure  160),  which  is  placed  in  a  large  vessel,  R,  fiDed 

Fig.  1 60. 


with  hot  water,  and  is  thus  kept  at  a  definite  temperature. 
C  is  a  calorimeter,  or  heat-measurer.  It  consists  of  three 
vessels  placed  one  within  another.  The  inner  one  is 
surrounded  with  water,  and  the  middle  one  with  air.  As 
air  is  a  very  poor  conductor,  all  the  heat  given  out  by  the 
inner  vessel  is  kept  in  the  water.  The  radiant  heat  of  R 
is  shut  off  from  C  by  the  screen  P.  When  the  cock  r  is 
opened,  the  liquid  in  the  vessel  O  runs  into  the  inner 
vessel  of  C,  and  there  gives  up  its  heat  to  the  water  in  the 
middle  vessel.  The  weight  of  the  water  in  this  vessel  is 


220 


HEAT. 


supposed  to  be  known,  and  its  temperature  at  the  be- 
ginning and  end  of  the  experiment  is  noted.  We  can 
then  find  how  many  units  of  heat  the  liquid  in  the  inner 
vessel  has  given  up  to  the  water,  and  also  how  many 
degrees  it  has  cooled.  By  finding  the  weight  of  the  liquid 
in  that  vessel,  we  can  find  how  many  units  of  heat  one 
pound  of  it  would  give  out  in  cooling  i°,  or  its  specific 
heat. 

It  is  found  in  this  way  that  the  specific  heat  of  a  sub- 
stance when  in  the  liquid  state  is  greater  than  when  in  the 
solid  state  ;  and  that  the  specific  heat  of  a  liquid  increases 
with  the  temperature,  and  more  rapidly  than  that  of  solids. 

210.  Specific  Heat  of  Gases.  —  Regnault  used  the  follow- 
ing method  for  finding  the  specific  heat  of  gases.  The  gas 
is  first  forced  into  a  large  receiver,  R>  (Figure  161),  where 

Fig.  161. 


it  is  kept  at  a  constant  temperature  by  the  water  surround- 
ing it.  On  opening  the  stopcock  /  the  gas  may,  by  an 
arrangement  at  ry  be  made  to  flow  out  through  the  pipe  in 
a  uniform  stream.  It  is  then  passed  through  the  coiled 
pipe  in  the  chamber  S,  where  it  is  heated  to  a  high  tem- 


HEAT. 


221 


perature,  which  is  measured  by  the  thermometer  T'.  It  is 
then  sent  through  the  calorimeter  C,  where  it  gives  up  its 
heat  to  the  water.  By  means  of  a  manometer  the  pressure 
of  the  gas  in  R  is  found  at  the  beginning  and  at  the  end 
of  the  experiment.  The  difference  of  pressure  enables  us 
to  find  the  weight  of  gas  which  has  passed  through  the 
calorimeter,  for  the  density  of  a  gas  is  inversely  propor- 
tional to  its  pressure.  If,  for  instance,  the  pressure  of  the 
gas  at  the  end  of  the  experiment  is  one  half  what  it  was  at 
the  beginning,  its  density  will  be  only  one  half;  and  there- 
fore one  half  of  the  gas  must  have  passed  out.  When  we 
know  the  weight  of  the  gas  which  has  passed  through  C, 
and  the  heat  it  has  given  up  to  the  water,  we  can  easily 
find  its  specific  heat. 

The  following  Table  gives  the  specific  heat  of  certain 
gases  and  vapors :  — 


Gas  or  Vapor. 

Equal  Vols. 

Equal  Weights. 

Air. 

O.237S 

Oxygen  

O.24.O? 

0.2171; 

Nitrogen      

0.2368 

O.24T.8 

Hydrogen 

O  23S9 

•j  4.OQO 

Chlorine  

O.2Q6A 

O.I2IO 

Bromine.    .  .       

o.  3040 

O.OS1?1? 

Nitrous  oxide 

O.744.7 

O.2262 

Nitric  oxide 

^•snni 

o  2406 

O  23.17 

Carbonic  oxide  

0.2370 

o  24^0 

Carbonic  acid.  ...             

O.33O7 

0.2169 

Bisulphide  of  carbon   . 

O.4I22 

0.1^69 

Ammonia                                    .  . 

O  2996 

Jr> 

o  ^084 

Marsh  gas 

O  3277 

O  ^929 

Olefiant  gas 

o  4160 

o  4040 

Water  

O.2Q8Q 

o  4805 

Alcohol  

O.7I7I 

O  4"?  34 

211.  Influence  of  the  State  of  a  Substance  on  its  Specific 
Heat.  —  The  same  body  has  a  higher  specific  heat  in  the 
liquid  than  in  the  solid  state ;  while  in  the  gaseous  con- 
dition, again,  its  specific  heat  is  less  than  when  it  is  liquid. 
Thus,  for  instance,  the  specific  heat  of  water  is  twice  as 


222 


HEAT. 


great  as  that  of  ice,  and  more  than  twice  as  great  as  that 
of  steam. 

The  following  Table  exhibits   the   dependence  of  the 
specific  heat  on  the  physical  state  of  the  substance  :  — 


j 

Specific  Heat. 

Solid. 

Liquid. 

Gaseous. 

Water 

o  ^040 

I  OOOO 

o  480*5 

Bromine  

008'?'? 

o  1060 

O.O^S 

Tin  

o  ex  62 

o  0637 

Iodine 

O  O<Jd.I 

o  1082 

Lead 

O  O1  1  A 

o  0402 

Alcohol  

O  ^47? 

O.4C74 

Bisulphide  of  carbon  .  .  . 

O  21^2 

o  1^60 

Ether  

O.IJ2QO 

O.47Q7 

SUMMARY. 

The  heat  which  a  body  absorbs  is  partially  used  in  raising 
its  temperature.  (202.) 

A  body  in  cooling  i°  gives  out  just  as  much  heat  as  it 
takes  to  warm  it  i°.  (203.) 

It  takes  a  different  amount  of  heat  to  raise  the  tempera- 
ture of  the  same  weight  of  different  substances  i°.  (204.) 

The  amount  of  heat  required  to  raise  the  temperature  of 
one  pound  of  water  i°  is  called  a  unit  of  heat.  (205.) 

The  amount  of  heat  required  to  raise  the  temperature  of 
one  pound  of  any  substance  i°,  expressed  in  thermal  units, 
is  called  its  specific  heat.  (206.) 

The  specific  heat  of  a  solid  may  be  found  by  the  method 
of  mixture  or  by  that  of  fusion.  (207,  208.) 

The  specific  heat  of  a  liquid  or  of  a  gas  may  be  found 
by  means  of  the  calorimeter.  (209,  210.) 

The  same  body  has  a  higher  specific  heat  in  the  liquid 
than  in  the  solid  state,  but  a  lower  specific  heat  when  a 
gas  than  when  a  liquid.  (211.) 


HEAT. 


223 


CHANGE  OF  STATE. 

212.  Heat  causes  Solids  to  melt.  —  Place  a  dish  of  water 
at  the  temperature  of  32°  and  a  dish  of  ice  at  the  same 
temperature  side  by   side  in  a  warm   room,   and   hold  a 
thermometer  bulb  in  each.     The  temperature  of  the  water 
will  gradually  rise,  while  that  of  the  ice  will  not  rise  until 
the  whole  is  melted.      The  heat,  then,   which  has   been 
absorbed  by  the  ice  has  melted  it,  or  changed  its  state. 

The   second  effect  of  heat  upon  a  body,   then,   is  to 
change  its  state. 

213.  The  Melting- Point.  —  Ice,  as  we  have  seen,  has  a 
temperature  of  32°.     Mercury  melts  at  — 38°;  and  alcohol 
at  a  temperature  lower  than  we  have  yet  been  able  to 
produce.     On  the  other  hand,  phosphorus  melts  at  m°; 
iron  at  2912° ;  and  charcoal  at  a  higher  temperature  than  we 
have  yet  been  able  to  produce.    Though  the  melting-points 
of  different  substances  vary  so  much,  that  of  any  one  sub- 
stance is,  under  the  same  circumstances,  always  the  same. 

The  following  Table  of  melting-points  is  from  Stewart:  — 


Name  of  Substance. 

Temperature  of 
melting-point  in 
degrees  Fahrenheit. 

Observer. 

Mercury  .                          .  . 

—37-9 
—  30.0 

H-  9-5 
32.0 
111.5 

136.0 
207.7 
239.0 
451.0 
512.0 
620.0 
680.0 
810.0 
1832.0 
2282.0 
2732.0 
2912.0 

Stewart. 
Regnault. 
Pierre. 

Schrotter. 

Regnault. 
« 

Person. 
«« 

Pouillet. 
<« 

« 
« 

Oil  of  vitriol 

Bromine  . 

Ice  

Phosphorus  

Potassium  

Sodium 

Sulphur  .  . 

Tin  

Bismuth  

Lead  

Zinc  . 

Antimony 

Silver  (pure)  

Gold  (pure)  

French  wrought  iron  .... 
English  wrought  iron  .... 

224  HEAT. 

Certain  bodies  become  soft  or  viscous  before  they  melt. 
If  a  substance  is  capable  of  assuming  a  viscous  or  semi- 
solid  state,  we  find  that  it  does  so  before  it  begins  to  melt, 
and  that  it  passes  from  a  solid  state  through  a  semi-solid 
viscous  state  to  that  of  a  liquid  of  evident  mobility.  Seal- 
ing-wax is  a  very  good  example  of  a  substance  of  this 
nature  ;  when  cold  it  is  quite  brittle,  when  heated  it  first 
grows  plastic,  and  finally  melts.  In  like  manner,  before 
fluidity  iron  becomes  soft  in  such  a  manner  that  pieces  may 
be  easily  welded  together  or  moulded  into  any  form  ;  and 
this  property  of  iron  greatly  enhances  its  value  in  the  arts. 
Other  instances  might  be  mentioned,  and  a  gradual  pas- 
sage from  the  solid  to  the  liquid  state  characterizes  a  large 
number  of  bodies.  Furthermore,  certain  substances,  even 
after  they  have  become  unmistakably  solid,  acquire  certain 
properties,  such  as  hardness  and  brittleness,  in  greater  per- 
fection as  the  temperature  continues  to  fall.  Indeed,  most 
hard  bodies  have  high  melting-points,  and  the  diamond, 
which  is  the  hardest,  is  not  susceptible  of  fusion  even  at 
a  very  high  temperature. 

214.  Latent  Heat  of  Liquids.  —  If  a  pound  of  ice  at  32° 
be  mixed  with  a  pound  of  water  at  212°,  the  temperature, 
when  the  ice  is  melted,  will  be  50.5°.     It  has  then  taken 
161.5  units  of  heat  to  melt  a  pound  of  ice  and  to  raise  its 
temperature  from  32°  to  50.5°,  or  18.5°.     It  therefore  takes 
143  units  of  heat  to  melt  a  pound  of  ice.     Heat  always 
disappears  in  melting  a  solid  ;  and  this  heat  is  called  the 
latent  heat  of  fusion,  or  the  latent  heat  of  the  liquid,  since  it 
is  concealed  in  the  liquid. 

By  the  latent  heat  of  a  liquid,  then,  we  mean  the  num- 
ber of  units  of  heat  required  to  melt  one  pound  of  the  sub- 
stance. Thus  the  latent  heat  of  water  is  143  units. 

When  the  liquid  passes  back  into  the  solid  state  again, 
its  latent  heat  reappears  as  sensible  heat. 

215.  How  to  find  the  Latent  Heat  of  Liquids.  —  The  readi- 


HEAT. 


225 


est  way  of  finding  the  latent  heat  of  a  liquid  is  to  place 
the  liquid  at  a  known  temperature  in  a  calorimeter  (209), 
allow  it  to  solidify,  and  observe  how  much  heat  it  gives 
out.  This  amount  will  be  its  latent  heat  plus  the  heat  it 
loses  in  cooling  down  to  its  final  temperature. 

If,  for  instance,  32  pounds  of  melted  lead  at  630°  be 
placed  in  a  calorimeter  and  allowed  to  cool  down  to  200°, 
it  will  give  out  439.664  units  of  heat.  Now  the  specific 
heat  of  lead  is  .0314,  and,  multiplying  this  by  32,  we  get 
i  unit  of  heat  (nearly).  The  32  pounds  of  lead,  then,  in 
cooling  i°  give  out  i  unit  of  heat ;  and  in  cooling  430°,  as 
in  the  above  experiment,  430  units.  439.664  —  430  = 
9.664  units,  which  is  the  latent  heat  of  lead. 

The  following  Table,  giving  the  latent  heat  of  fusion  of 
certain  substances,  is  taken  from  Stewart :  — 


Substance. 

Latent  Heat  of  one  pound. 

Thermal  Units. 

Water  =  i. 

Water  

79.250 
5-°34 

9.368 

62.975 

47-371 
14.252 

12.640 

5.369 

28.130 
13.660 

21.070 
2.830 

I.OOO 

0.063 
0.118 
0.794 
0.598 
0.179 
0.159 

0.067 

°-355 
0.172 
0.266 
o-035 

Phosphorus  .  .      .                

Sulphur.  . 

Nitrate  of  sodium  

Nitrate  of  potassium   . 

Tin  

Bismuth  . 

Lead  

Zinc  

Cadmium  

Silver  

Mercury  

In  this  table  the  unit  of  heat  is  the  amount  of  heat 
required  to  raise  the  temperature  of  one  pound  of  water  i° 
Centigrade,  which  is  -|  of  the  English  unit  of  heat  based 
upon  the  Fahrenheit  scale.  The  numbers  in  the  first  col- 
umn can  be  changed  to  the  English  units  by  multiplying 
them  by  f . 

10*  o 


226 


HEAT. 


2 1 6.  Heat^ causes  Liquids  to  boil. — Under  the  ordinary 
pressure,  if  water  be  raised  to  a  temperature  of  212°,  it  be- 
gins to  boil,  and  its  temperature  then  remains  the  same 
until  it  is  all  converted  into  steam.  The  heat,  then,  which 
the  water  absorbs  changes  it  from  the  liquid  to  the  gaseous 
state.  Other  liquids  can  be  made  to  boil,  but  at  very 
different  temperatures.  Any  given  liquid,  under  the  same 
circumstances,  always  boils  at  the  same  temperature. 

The  following  Table  gives  the  boiling-points  of  several 
liquids  :  — 


Name  of  Substance. 

Boiling-Point 
Fahrenheit. 

Observer. 

Ether 

QA    g 

Kopp 

Bisulphide  of  carbon    

118  5 

Pierre. 

Formic  ether                       .    . 

127  7 

Bromine 

14.^  A. 

(i 

\Vood-spirit 

IAQ  Q 

Kopp 

Acetic  ether  

164.  Q 

Pierre 

Alcohol  . 

1  73  I 

Benzole 

176  8 

Water  

212  O 

Formic  acid  .... 

221  £ 

« 

Acetic  acid 

2/1'?  i 

« 

Sulphuric  acid  

64.0  o 

Marignac. 

Mercury  

6620 

Recnault 

217.  Latent  Heat  of  Gases.  —  If  a  thermometer  be  held 
in  the  steam  just  over  boiling  water,  it  will  indicate  a  tem- 
perature of  212°.  Now,  as  water  is  receiving  heat  all  the 
time  it  is  boiling,  this  heat  must  be  latent  in  the  steam. 
The  latent  heat  of  steam  or  of  any  other  vapor  is  found 
by  boiling  the  liquid,  and  sending  the  vapor  through  a 
calorimeter.  The  steam  is  reduced  to  a  liquid,  and  cooled 
to  a  certain  point.  The  amount  of  heat  given  out  by  the 
cooling  of  the  liquid  is  readily  calculated,  and  the  surplus 
is  the  latent  heat  of  the  vapor. 

In  the  following  Table  (from  Stewart)  the  latent  heat  of 
several  vapors  is  given  :  — 


HEAT. 


227 


Substance. 

Latent  Heat  of  one  pound. 

In  Thermal  Units. 

Steam  =  i. 

Water 

535-90 
263.70 
202.40 
105.30 
92.68 

90.45 
86.67 
45.60 
30.53 

I.OOO 
0.492 
0.378 
0.196 

0.173 
0.169 
O.I62 
0.085 
0.057 

Wood-spirit  

Alcohol  

Formic  ether. 

Acetic  ether  

Ether  

Bisulphide  of  carbon 

Bromine  

Perchloride  of  tin..                   .    . 

The  units  in  this  table  are  the  same  as  in  the  table  in 
section  215. 

218.  The  State  of  a  Body  depends  upon  its  Temperature. 
—  When   a   solid   is   heated,  its  temperature  rises  till  it 
reaches   the   melting-point,   where   it    remains    stationary 
until  the  solid  is  melted.      It  then   rises   again  until  it 
reaches  the  boiling-point,  where  it  again  remains  station- 
ary until  the  liquid  is  converted  into  a  gas.     When  a  gas 
is  sufficiently  cooled,  it  goes  through  the  same  changes  in 
the  reverse  order. 

It  is  owing  to  the  fact  that  different  substances  have 
very  different  boiling-points  that  they  can  exist  in  nature, 
some  as  solids,  some  as  liquids,  and  some  as  gases. 
Hydrogen  and  oxygen  are  only  the  steam  of  liquids  which 
boil  at  a  very  low  temperature,  perhaps  four  or  five  thou- 
sand degrees  below  zero. 

219.  The  Boiling-Point  of  Waterfalls  as  the  Pressure  on 
its   Surface  diminishes.  —  Fill   a  flask   two  thirds  full  of 
water,  boil  it  for  some  time,  cork  it  tightly,  removing  it  at 
the  same  time  from  the  source  of  heat,  and  invert  it,  as 
shown  in  Figure  162.     Pour  cold  water  upon  the  flask, 
and  it  begins  to  boil  again,  and  the  boiling  may  be  con- 
tinued until  the  temperature  of  the  water  in  the  flask  has 
fallen  considerably  below  212°. 


228 


HEAT. 


Fig.  162. 


At  first  the  upper  part  of  the  flask  is  full  of  steam,  whose 
elastic  force  causes  it  to  press  upon  the  water.  When  cold 
water  is  poured  upon  the  flask,  this  steam  is  condensed, 
the  pressure  is  diminished,  and  the  water  boils,  though  at 
a  lower  temperature. 

The  height  of  a  mountain  can  be  estimated  with  con- 
siderable accuracy  by 
the  difference  between 
the  boiling-points  at  its 
summit  and  at  its  base. 
Thermometers  have 
been  constructed  on 
which  are  marked,  not 
the  degrees  of  temper- 
ature, but  the  number 
of  feet  of  elevation. 
When  the  bulb  of  such  a 
thermometer  is  plunged 
into  boiling  water,  the 
mercury  in  the  stem 
shows  the  elevation  of 
the  place. 

It  has  already  been 
shown  that  steam  occu- 
pies very  much  more 
space  than  the  same  weight  of  water,  and  also  that  there 
is  no  cohesion  among  its  molecules.  When,  therefore, 
water  boils,  both  the  cohesion  of  the  liquid  and  the 
pressure  of  the  atmosphere  must  be  overcome,  since  both 
of  these  tend  to  keep  the  molecules  together.  Hence, 
when  either  the  cohesive  force  or  the  external  pressure 
is  changed,  the  boiling-point  will  also  change. 

220.  The  Boiling- Point  of  Water  is  raised  by  increasing 
the  Cohesion  of  its  Molecules.  —  When  any  salt,  as  saltpetre, 
is  dissolved  in  water,  the  boiling-point  is  raised.  This  is 


HEAT.  229 

probably  owing  to  the  fact  that  the  presence  of  the  salt 
causes  the  molecules  to  cohere  more  strongly. 

Again,  it  is  well  known  that  water  absorbs  air  and  other 
gases ;  and  the  elastic  force  of  these  gases,  which  tends  to 
separate  the  molecules,  partially  overcomes  their  cohesion. 
Hence  we  should  expect  that  the  cohesive  force  of  water 
would  be  increased  by  removing  the  air  from  it. 

The  tube  in  Figure  163  is  partially  rilled  with  water  from 
which  the  air  has  been  removed  by  long  boiling.  While 
the  water  is  still  boiling,  the  tube  is  sealed  at  C,  so  that 
there  is  no  air  in  the  tube.  When  the  water  is  brought 
into  the  arm  A  B  and  made  to  come  thoroughly  in  contact 
with  the  end  A,  the  tube  may  be  inverted,  as  shown  in  the 
figure,  and  the  water  will  not  flow  out  Fi  i6 

from  this  arm.  The  cohesive  force 
among  the  molecules  is  now  so  great 
that  they  stick  together,  somewhat  like 
those  of  a  solid. 

When  the  water  is  made  to  flow 
from  one  end  of  such  a  tube  to  the 
other,  it  strikes  with  a  sharp  metallic 
click,  and  not  with  the  usual  splashing 
sound.  The  latter  is  caused  by  the  cushion  of  air  which 
separates  the  water  and  the  glass  against  which  it  strikes. 

Since  the  removal  of  the  air  from  water  increases  the 
cohesion  among  the  molecules,  it  raises  the  boiling-point 
of  the  liquid.  In  this  way  it  has  actually  been  raised  to 
275°.  But  when  water  thus  freed  from  air  does  boil,  it  is 
converted  into  steam  with  explosive  violence.  This  may 
be  the  cause  of  some  boiler  explosions,  the  air  having 
been  removed  from  the  water  by  long  foiling. 

221.  The  Nature  of  the  Vessel  in  which  Water  is  boiled 
changes  the  Boiling- Point.  —  If  a  glass  vessel  be  carefully 
cleansed  from  all  grease  by  means  of  sulphuric  acid,  it 
will  be  found  that  it  requires  a  temperature  2°  or  3°  higher 


230  HEAT. 

to  boil  water  in  it  than  in  a  tin  vessel.  Other  experiments 
show  that  the  boiling-point  changes  with  the  material  of 
the  vessel  used.  This  is  probably  owing  to  the  difference 
in  the  adhesive  force  between  the  water  and  the  vessel. 

222.  The  Spheroidal  State.  —  If  two  or  three  drops  of 
water  be  poured  into  a  red-hot  metallic  cup,  they  gather 
into  a  globule,  which  runs  about  without  boiling.  In  this 
case  the  water  is  said  to  be  in  the  spheroidal  state. 

Turn  a  cup  c  bottom  up  (Figure  164),  heat  it  to  redness, 

Fig.  164. 


and  carefully  put  a  drop  of  water  d  upon  it  by  means  of  a 
dropping-tube.  Place  behind  the  drop  a  piece  of  platinum 
wire  a  b,  heated  to  a  white  heat  by  means  of  the  electric 
current.  It  will  be  found,  if  the  eye  be  placed  at  <?,  that  the 
platinum  wire  can  be  seen  between  the  drop  and  the  cup, 
showing  that  the  drop  does  not  touch  the  cup. 

That  water  in  the  spheroidal  state  does  not  touch  the 
Fig.  165.  heated   surface   may  be 

shown  in  another  way. 
B,  in  Figure  165,  is  a 
heated  metallic  cup  ;  A 
is  a  galvanic  cell,  one 
pole  of  which  is  con- 
nected with  a  galva- 
nometer and  the  other 
with  the  platinum  point 
b.  The  cup  B  is  also 
connected  with  the  galvanometer  G.  A  little  water  is 
poured  into  the  cup,  and  the  platinum  point  introduced 


HEAT.  231 

into  it.  If  the  drop  touched  the  cup,  the  circuit  would  now 
be  complete  ;  but  the  needle  of  the  galvanometer  does  not 
move,  showing  that  the  circuit  is  incomplete,  and  that  the 
drop  does  not  touch  the  cup.  But  if  the  cup  be  allowed 
to  cool,  the  needle  soon  swings  round,  showing  that  the 
drop  has  come  in  contact  with  the  surface  of  the  cup.  At 
the  same  instant  the  drop  is  converted  into  a  cloud  of 
steam. 

The  explanation  of  the  spheroidal  state  is  this :  as  soon 
as  the  drop  comes  near  the  heated  cup,  steam  is  generated 
beneath  it,  and  this  steam,  acting  like  an  elastic  spring, 
lifts  the  drop  from  the  surface.  As  the  cup  cools,  this 
spring  gives  way,  and  the  water,  on  touching  the  surface, 
is  suddenly  converted  into  steam. 

Boiler  explosions  are  probably  often  caused  by  the 
water's  assuming  the  spheroidal  state,  and  then  suddenly 
passing  into  steam. 

223.  Evaporation.  —  If  water   is   exposed   in   an   open 
vessel  at  the  ordinary  temperature,  it  gradually  disappears, 
passing  off  in  the  form  of  vapor.     This  vapor  is  formed 
slowly  and  only  at  the  surface  ;  while,  in  boiling,  steam  is 
formed  rapidly  and  throughout  the  liquid.     Water  is  thus 
evaporated  into  the  atmosphere  at  all  temperatures,  but 
more  rapidly  as  the  temperature  rises. 

224.  Condensation.  — A  gas  condenses  at  the  same  point 
at  which  its  liquid  boils;  and,  as  pressure  raises  the  boiling- 
point  of  a  liquid,  it  also  raises  the  point  at  which  a  gas 
will  condense.     Under  the  combined   action  of  pressure 
and  cold,  almost  every  known  gas  has  been  liquefied.     The 
only  exceptions  are  oxygen,  hydrogen,  nitrogen,  nitric  ox- 
ide, carbonic  oxide,  and  marsh  gas. 

Faraday  was  the  first  who  succeeded  in  liquefying  gases 
in  this  way.  Carbonic  acid  is  now  condensed  in  large 
quantities.  Figure  166  shows  a  part  of  the  apparatus  in- 
vented by  Thilorier  for  this  purpose. 


232 


HEAT. 


Fig.  1 66. 


The  gas  is  generated  in  a  strong  iron  vessel  called  the 
generator,  into  which  the  materials  for  making  the  gas  are 
put.  This  generator  is  connected  with  an  equally  strong 
iron  vessel  called  the  receiver,  (shown  in  the 
figure,)  which  is  kept  cool,  and,  when  sufficient 
gas  has  been  generated,  it  condenses  in  the 
receiver.  The  two  vessels  are  now  separated, 
and  a  fresh  charge  introduced  into  the  gener- 
ator, and  the  gas  is  condensed  in  the  receiver 
as  before,  until  at  last  a  large  quantity  of 
liquefied  gas  has  been  obtained. 

225.  Freezing- Mixtures.  —  When  a  solid 
melts,  or  a  liquid  evaporates,  a  large  amount 
of  heat  is  rendered  latent.  Advantage  is 
taken  of  this  fact  to  obtain  an  artificial  reduc- 
tion of  temperature.  One  of  the  most  com- 
mon freezing-mixtures-  is  composed  of  salt 
and  pounded  ice.  The  substance  to  be  frozen 
is  placed  in  a  small  vessel  which  is  put  in  a  larger  one 
and  packed  round  with  this  mixture.  The  ice  rapidly 
melts,  and  in  doing  so  absorbs  a  large  amount  of  heat, 
thus  reducing  the  temperature  of  the  inner  vessel. 

A  much  greater  degree  of  cold  can  be  produced  by  the 
rapid  evaporation  of  a  liiquid  than  by  the  melting  of  a 
solid.  It  will  be  seen  from  Figure  166  that  in  the  interior 
of  the  receiver  there  is  a  tube  which  descends  below  the 
level  of  the  liquid.  When  the  cock  is  open,  the  pressure 
of  the  gas  drives  the  liquid  with  great  force  up  the  tube 
and  out  through  the  fine  nozzle  in  which  it  terminates. 
The  liquid  as  it  issues  evaporates  so  fast  that  part  of  it 
is  frozen,  and  the  solidified  gas  may  be  collected  in  the 
form  of  a  snow-white  powder.  This  powder  evaporates 
very  slowly,  and  may  therefore  by  proper  precautions  be 
preserved  for  a  considerable  length  of  time.  It  may  also 
be  handled  with  impunity,  and  may  even  be  laid  upon  the 


HEAT.  233 

tongue  without  a  disagreeable  sensation  of  cold,  although 
its  temperature  is  extremely  low,  perhaps  even  — 106°  F. 
The  reason  of  this  absence  of  the  feeling  of  cold  is  want 
of  contact  between  the  solid  and  the  tongue  or  the  hand. 
The  solid  is  actually  in  the  spheroidal  state. 

If  the  solid  acid  be  mixed  with  ether,  it  evaporates 
rapidly,  and  a  great  degree  of  cold  is  the  result.  By 
means  of  such  a  mixture  20  or  30  pounds  of  mercury  may 
be  readily  frozen.  If  the  mixture  be  placed  under  an 
exhausted  receiver,  the  evaporation  is  greatly  quickened, 
and  a  much  greater  degree  of  cold  is  obtained.  Faraday 
thus  reached  a  temperature  of  — 166°  F. 

A  still  lower  temperature,  of  — 220°,  has  been  obtained 
by  Natterer  by  placing  a  mixture  of  liquid  nitrous  oxide  and 
bisulphide  of  carbon  in  an  exhausted  receiver. 


SUMMARY. 

The  heat  which  a  body  absorbs  is  sometimes  used  in 
changing  its  state.  (212.) 

The  melting  and  boiling  points  are  the  same  for  the 
same  substance  under  the  same  pressure  ;  but  those  of 
different  substances  are  different  (213,  216.) 

When  a  substance  melts  or  boils,  a  certain  definite 
amount  of  heat  is  rendered  latent.  The  heat  thus  ren- 
dered latent  is  called  the  latent  heat  of  the  liquid,  or  of 
the  vapor,  or  gas.  (214,  217.) 

The  latent  heat  of  a  liquid  or  a  vapor  can  be  found  by 
means  of  the  calorimeter. 

The  latent  heat  of  water  is  higher  than  that  of  any 
other  liquid  ;  and  that  of  steam  is  higher  than  that  of 
any  other  vapor.  (215,  217.) 

The  boiling-point  of  water  is  raised  by  increasing  the 
pressure,  and  by  freeing  the  water  from  air.  (219,  220.) 

When  water  is  put  into  a  red-hot  vessel,  it  is  prevented 


234  HEAT. 

from  coming  in  contact  with  the  heated  surface  by  a  Jayer 
of  steam,  and  is  said  to  be  in  the  spheroidal  state.  (222.) 

Liquids  evaporate  at  all  temperatures,  but  more  rapidly 
as  the  temperature  rises.  (223.) 

Vapors  condense  at  the  same  point  as  that  at  which 
their  liquids  boil.  (224.) 

In  the  various  freezing-mixtures,  advantage  is  taken  of 
the  fact  that  heat  is  rendered  latent  in  the  melting  of  solid:* 
and  in  the  evaporation  of  liquids.  (225.) 

EXPANSION. 

226.  Solids  are  expanded  by  Heat.  —  If  a  brass   ball 
which  will  just  pass  through  a  ring  be  heated,  it  will  no 
longer  pass  through  the  ring.     It  has  been  expanded  by 
the  heat.     In  like  manner  all  solids  are  found  to  be  ex- 
panded by  heat. 

227.  Different  Solids  expand  unequally  for  the  Same  Rise 
of  Temperature.  —  If  a  bar  of  iron  and  one  of  copper  be 
riveted  together  and  then  plunged  in  boiling  water,  so  that 
the  temperature  of  both  may  be  raised  to  the  same  point, 
the  compound  bar  will  become  curved,  the  copper  being 
the  convex  side.      This  is  because  copper  is   expanded 
more  than   iron  for  the'  same  rise  of   temperature.      On 
comparing  different  solids  we  find  that  scarcely  any  two 
are  expanded  alike  by  heat. 

228.  Liquids  are  expanded  by  Heat.  —  Fill  a  test-tube 
with  water,  and  then  close  it  with  a  rubber  cork  through 
which  passes  a  fine  glass  tube.      Plunge  the  test-tube  in 
boiling  water,  and  the  liquid  will  rise  in  the  tube,  showing 
that  it  has  been  expanded  by  heat. 

229.  Different  Liquids   expand   unequally  for  the  Same 
Rise  of  Temperature.  —  Fill  a  second  test-tube  with  alcohol, 
and  plunge  both  into  boiling  water.     The  alcohol  will  rise 
higher  in  the  tube  than  the  water  will,  showing  that  it  is 


HEAT.  235 

expanded  more  by  the  heat.     Different  liquids,  then,  ex- 
pand unequally  for  the  same  rise  of  temperature. 

230.  Gases  are  expanded  by  Heat.  —  Close  a  pint  flask 
with  a  cork  through  which  passes  a  bent  tube,  and  connect 
the  tube  with  a  jar  inverted  over  water.     Plunge  the  flask 
into  boiling  water,  and  bubbles  of  air  rush  over  into  the 
jar.     This  experiment  shows  that  air  is  expanded  by  heat. 
The  same  is  found  to  be  true  of  all  other  gases. 

231.  Different  Gases  expand  equally  for  the  Same  Rise  of 
Temperature.  —  Fill  now  the  same  flask  with  hydrogen  or 
oxygen,  connect  it  with  the  same  jar  as  before,  and  again 
plunge  the  flask  into  boiling  water.     Precisely  the  same 
amount  of  gas  will  pass  over  as  at  first,  showing  that  these 
gases  expand  equally  for  the  same   rise  of  temperature. 
The  same  is  true  of  other  gases. 

Solids,  liquids,  and  gases  are,  then,  expanded  by  heat ; 
solids  and  liquids  unequally,  and  gases  equally,  for  the 
same  rise  of  temperature. 

232.  How  to  find  the  Coefficient  of  Expansion  for  Mercury. 
—  Copper  expands  .000051  of  its  volume  for  a  rise  of  i° 
Centigrade.     The  amount  a  body  expands  for  a  rise  of  i° 
C.  is  called  its  coefficient  of  expansion.     The  coefficient  of 
expansion  for  copper,  then,  is  .000051. 

When  this  coefficient  is  known,  the  expansion  of  any 
body  for  any  given  rise  of  temperature  can  be  readily 
calculated. 

A  and  B  (Figure  167)  are  upright  glass  tubes  connected 
at  the  bottom.  Both  are  surrounded  by  metallic  cases,  one 
of  which,  Z>,  is  filled  with  pounded  ice,  and  the  other,  T, 
with  oil.  The  latter  case  is  enclosed  in  a  furnace,  so  that 
its  temperature  can  be  raised  to  any  desired  point.  The 
density  of  the  mercury  in  the  tube  B  will  diminish  in  the 
exact  ratio  of  its  expansion,  and  the  temperature  of  the 
mercury  in  the  tube  A  is  always  at  the  freezing-point.  It 
will  therefore  rise  in  the  other  tube  in  proportion  as  it 


236  HEAT. 

expands  ;  that  is,  if  the  mercury  in  B  should  be  expanded 
so  as  to  double  its  volume,  it  would  stand  twice  as  high  in 
that  tube  as  in  A,  since  its  density  would  be  only  half  as 
great.  By  noticing,  then,  the  difference  in  the  height  of 
the  mercury  in  the  two  tubes  for  any  rise  of  temperature, 

Fig.  167. 


we  can  ascertain  the  expansion  of  the  mercury ;  and  this 
expansion,  divided  by  the  number  of  degrees  the  tempera- 
ture has  risen,  will  give  the  coefficient  of  expansion. 

233.  How  to  find  the  Coefficient  of  Expansion  for  any 
Liquid.  —  Let  a  glass  bulb  having  a  projecting  tube,  be 
filled  with  any  liquid  and  be  heated.  The  liquid  will  at 
first  fall  in  the  tube,  and  then  begin  to  rise  and  continue  to 
rise  steadily  as  the  temperature  increases.  The  falling  of 
the  liquid  at  first  is  owing  to  the  fact  that  the  glass,  being 
first  heated,  expands  before  the  liquid  does.  After  this  the 
liquid  expands  more  rapidly  than  the  glass,  and  therefore 
rises  in  the  tube. 

The  expansion  of  a  liquid  as  measured  in  such  a  bulb 


HEAT.  237 

is  only  its  apparent  expansion.     Its  real  expansion  is  this 
apparent  expansion  plus  the  expansion  of  the  bulb. 

The  expansion  of  the  bulb  can  be  found  by  means  of 
mercury.  In  Figure  168  we  have  a  bulb  with  a  projecting 
tube  drawn  out  to  a  fine  point.  This  bulb  is  first  weighed, 

Fig.  168. 


and  then  filled  with  mercury  and  weighed  again.  The 
difference  of  these  weights  is  the  weight  of  the  mercury  at 
the  ordinary  temperature.  The  bulb  is  now  heated,  and  a 
part  of  the  mercury  runs  out.  The  bulk  of  the  mercury 
which  runs  out  is  equal  to  the  excess  of  the  expansion  of 
the  mercury  over  that  of  the  bulb.  Now  we  know  the 
real  expansion  of  mercury,  and  the  excess  of  this  over  its 
apparent  expansion,  as  just  found,  is  the  expansion  of  the 
bulb.  This  expansion,  plus  the  apparent  expansion  of  any 
liquid  put  into  the  bulb,  gives,  as  we  have  seen,  the  real 
expansion  of  the  liquid  for  any  rise  of  temperature  ;  and 
this  divided  by  the  number  of  degrees  the  temperature  has 
risen  gives  the  coefficient  of  expansion. 

234.  How  to  find  the  Coefficient  of  Expansion  for  any 
Solid.  —  The  volume  and  weight  of  the  solid  whose  ex- 
pansion is  to  be  found  are  first  ascertained.  It  is  then  put 
into  a  glass  tube,  of  known  weight,  which  is  filled  with 
mercury  and  drawn  out  to  a  fine  point.  The  weight  of  the 
whole,  minus  the  weight  of  the  tube  and  the  solid,  is  the 
weight  of  the  mercury.  The  whole  is  now  heated  to  a 
certain  temperature,  and  the  mercury  which  runs  out  is 
weighed.  Now,  since  we  know  the  rate  of  expansion  of 
the  glass  and  of  the  mercury,  we  know  how  much  mercury 


238 


HEAT. 


should  have  run  out  had  the  solid  not  expanded  at  all  ; 
and  the  excess  of  the  mercury  which  actually  runs  out 
over,  this  amount  is  equal  to  the  expansion  of  the  solid. 
This  divided  by  the  number  of  degrees  the  temperature 
has  risen  gives  the  coefficient  of  expansion. 

235.  How  to  find  the  Coefficient  of  Expansion  for  Air  and 
other  Gases.  —  In  Figure  169  b  is  a  large  glass  bulb  filled 
with  air  and  connected  by  a  glass  tube  with  the  upright  tube 
T.  The  latter  opens  into  a  vessel  of  mercury,  as  does  also 

Fig.  169. 


the  tube  T'.  By  means  of  the  screw  S  the  mercury  can  be 
kept  at  the  same  height  in  the  two  tubes.  The  bulb  is 
first  surrounded  with  melting  ice,  and  the  mercury  in  the 
two  tubes  is  brought  to  the  same  level.  The  bulb  is  next 
immersed  in  steam,  and  the  mercury  in  the  tubes  again 
brought  to  the  same  level.  The  difference  of  the  heights 


HEAT.  239 

of  the  mercury  in  the  two  cases  is  equal  to  the  expansion 
of  the  air  for  a  rise  of  temperature  between  32°  and  212° 
F.,  and  from  this  we  can  easily  find  its  coefficient  of  ex- 
pansion. Since  the  air  on  expanding  partially  fills  the 
tube  T,  it  is  necessary  that  the  tubes  T  and  T'  should  be 
surrounded  with  boiling  water,  in  ordf^r  that  all  the  air 
may  be  kept  at  the  same  temperature. 

It  is  found  in  this  way  that  air  expands  ,367  of  its  vol- 
ume for  a  rise  of  temperature  from  32°  to  212°. 

The  following  Table  shows  the  expansion  of  .•»eve**ai 
gases  for  this  rise  of  temperature  :  — 

Hydrogen 0.3661 

Atmospheric  air 0.3670 

Carbonic  oxide 0.3669 

Carbonic  acid 0.3710 

Nitrous  oxide °-37I9 

Sulphurous  acid 0.3903 

Cyanogen 0.3877 

It  will  be  observed  that  hydrogen,  carbonic  oxide,  and 
atmospheric  air,  gases  which  cannot  be  condensed  and 
whose  temperature  must  therefore  be  far  above  the  boiling- 
points  of  their  liquids,  expand  almost  exactly  alike,  while 
the  other  gases,  which  can  easily  be  condensed  and  must 
therefore  be  near  their  boiling-points,  expand  more  rapidly 
and  somewhat  more  unequally.  This  is  probably  because 
the  molecules  in  the  latter  are  still  so  near  together  that 
they  exert  considerable  influence  on  one  another.  At  a 
greater  distance  from  the  boiling-point  the  molecules  may 
get  so  far  apart  that  they  exert  no  sensible  influence  upon 
one  another.  Such  gases  are  called  perfect  gases. 

236.  When  a  Gas  is  not  allowed  to  expand,  its  Elasticity  is 
increased  by  Heat.  —  As  the  bulb  in  Figure  169  becomes 
heated,  the  expansion  of  the  gas  drives  the  mercury  from 
the  tube  T.  The  mercury  can,  however,  be  kept  at  the 
same  height  by  increasing  the  pressure  upon  the  mercury 


240  HEAT. 

in  the  box  by  means  of  the  screw  S.  This  increase  of 
pressure  will  also  cause  the  mercury  to  rise  in  the  tube 
T'.  The  difference  of  height  in  the  columns  of  mercury 
in  the  tubes  shows  how  much  the  elastic  force  of  the  gas 
is  increased.  In  this  way  it  is  found  that  the  elasticity  of 
air  when  not  allowed  to  expand  is  increased  about  .367 
for  a  rise  of  temperature  from  32°  to  212°. 

SUMMARY. 

The  heat  absorbed  by  a  body  is  used  partially  in  push- 
ing the  molecules  apart,  or  expanding  it.  (226.) 

Different  solids  and  liquids  expand  unequally,  and  dif- 
ferent gases  equally,  for  the  same  rise  of  temperature. 
(227,  231.) 

The  coefficient  of  expansion  for  a  body  is  the  amount  it 
expands  for  a  rise  of  temperature  of  i°  C.  (232  -  235.) 

When  a  gas  is  not  allowed  to  expand,  its  elasticity  is 
increased  by  heat.  (236.) 

CONVECTION. 

237.  We  have  now  .seen  that  the  molecules  of  a  body 
are  separated  when  it  becomes  heated ;  and,  since  the  mole- 
cules of  liquids  and  gases  are  free  to  move,  this  expansion 
ought,  when  they  are  heated  unequally  in  different  parts, 
to  create  currents  ;  for  the  unexpanded  and  heavier  por- 
tions will  tend  to  displace  the  lighter  ones  and  to  compel 
them  to  rise.     As  these  heavier  portions  become  heated, 
they  will  in  turn  tend  to  rise  and  give  place  to  colder  por- 
tions ;  and  so  on. 

These  currents,  of  course,  tend  to  distribute  the  heat,  and 
this  mode  of  distribution  is  called  convection. 

238.  Convection  of  Liquids.  —  In  Figure  170  we  have  a 
glass  beaker  filled  with  water  heated  by  a  lamp  below.     A 


HEAT. 


241 


little  sawdust  is  added  to  the  water,  and  its  motions  show 
that  a  current  is  passing  up  the  centre  of  the  vessel  and 
down  at  the  sides,  as  indicated  by  the  arrows  in  the 
figure.  Each  molecule  is  thus  seen  to  come  to  the  bottom 
to  get  heated,  and  then  to  return  Fig  1?a 

to  the  surface.  It  is  in  this  way 
that  water,  which  is  so  bad  a 
conductor,  is  so  readily  heated 
when  the  heat  is  applied  below. 

239.  Oceanic  Currents. — Oce- 
anic currents  are  produced  by 
convection.  The  temperature 
of  the  sea  in  the  tropics  is 
about  50°  higher  than  at  the 
poles,  and  the  specific  gravity 
of  the  water  is  therefore  much 
less.  To  restore  the  equilibri- 
um, the  warmer  and  lighter  wa- 
ter of  the  tropical  regions  flows  towards  the  poles,  and  the 
colder  and  denser  water  of  the  polar  regions  flows  towards 
the  equator.  If  the  whole  earth  were  covered  with  water 
of  the  same  saltness,  we  should  everywhere  have  a  surface- 
current  from  the  equator  towards  the  poles,  and  an  under- 
current from  the  poles  towards  the  equator.  But  owing  to 
the  obstructions  offered  by  the  land  and  by  the  inequalities 
in  the  bed  of  the  ocean,  and  to  the  different  degrees  of 
saltness,  and  therefore  of  density,  in  different  parts  of  the 
sea,  these  two  great  currents  are  broken  up  into  innumer- 
able currents  and  counter-currents,  which  diversify  the  face 
of  the  ocean  and  mark  out  the  highways  of  commerce. 

The  most  remarkable  of  these  currents  is  the  GulJ 
Stream,  which  issues  from  the  Gulf  of  Mexico,  flows  north- 
ward off  the  coast  of  the  United  States,  and,  crossing  the 
Atlantic  in  a  northeasterly  direction,  washes  the  western 
coast  of  Europe. 

ii  p 


242  HEAT. 

240.  Convection  of  Gases.  —  If  a  lighted  candle  be  put 
in  a  beam  of  solar  or  electric  light  which  is  thrown  upon  a 
screen  by  means  of  a  lens,  the  currents  of  air  which  are 
streaming  up  around  the  flame  can  be  readily  seen. 

Again,  if  a  lighted  candle  be  held  in  the  crack  of  a  door 
which  opens  from  a  warm  into  a  cold  room,  the  flame  will 
be  blown  outward  at  the  top  of  the  door  and  inward  at  the 
bottom,  while  half-way  up  it  will  burn  steadily.  A  current 
of  cold  air  is  thus  seen  to  be  passing  into  the  room  at  the 
bottom,  driving  out  a  current  of  warm  air  at  the  top. 

It  is  mainly  by  convection  that  the  air  in  a  room  is 
heated.  The  air  next  the  stove  is  heated  and  expanded, 
and  then  forced  upward  by  the  current  of  colder  air. 

When  a  building  is  heated  by  a  furnace,  this  is  placed  in 
the  cellar  and  encased  in  brick-work  or  in  sheet-iron.  The 
space  between  the  fire-pot  and  the  casing  is  connected  by 
means  of  the  air-box  with  the  outer  atmosphere,  and  by 
means  of  flues  or  pipes  with  the  rooms  to  be  heated.  The 
air  about  the  fire-pot  first  becomes  heated,  and  is  driven  up 
through  the  pipes  by  the  cold  air  from  without. 

SUMMARY. 

When  a  gas  or  a  liquid  is  heated  beneath  its  surface, 
currents  are  produced  which  distribute  heat  by  convection. 

It  is  in  this  way  that  the  Gulf  Stream  and  other  oceanic 
currents  are  produced.  (237  -  240.) 

THE   RELATION   OF   WATER  TO   HEAT. 

241.  The  High   Specific  and  Latent  Heat  of  Water.  — 
Water,  because  of  its  specific  and  latent  heat,  which  are 
higher  than    those    of  any  other  liquid,  exerts  a  marked 
influence  upon  climate.      It  makes  the  transition  from  win- 
ter to  summer  and  from  summer  to  winter  more  gradual. 


HEAT.  243 

In  the  spring,  when  the  snow  begins  to  melt,  a  large  amount 
of  heat  is  absorbed  from  the  air  and  rendered  latent. 
After  the  snow  and  ice  are  all  melted,  such  is  the  specific 
heat  of  water  that  it  requires  a  great  deal  of  heat  to  raise 
its  temperature.  In  the  fall,  on  the  other  hand,  as  the 
water  cools  down  and  freezes,  it  gives  out  all  the  heat 
which  it  had  absorbed  and  rendered  latent  in  the  spring. 

242.  The  Irregular  Expansion  and  Contraction  of  Water. 
—  Bodies,  as  we  have  seen,  usually  contract  when  cooled. 
Liquids  continue  to  contract,  not  only  until  they  are  frozen, 
but  even  after  freezing.  Fill  a  test-tube  with  water  at  a 
temperature  of  70°  and  close  it  with  a  rubber  cork  through 
which  passes  a  fine  glass  tube.  Press  the  cork  in  so  that 
the  water  shall  rise  in  the  tube.  Plunge  the  tube  into  a 
freezing  mixture,  and  the  water  gradually  falls  until  its 
temperature  is  about  39°.  It  then  slowly  rises  until  its 
temperature  is  32°.  It  now  begins  to  freeze,  and  suddenly 
expands.  If,  therefore,  water  at  the  temperature  of  39°  be 
either  warmed  or  cooled,  it  expands.  This  temperature  is 
hence  called  the  point  of  maximum  density  of  water. 

This  expansion  of  water  in  freezing  is  often  illustrated 
by  the  bursting  of  pipes  and  vessels  in  which  water  is 
allowed  to  freeze.  Water  is  the  only  liquid  which  has  such 
a  point  of  maximum  density,  and  there  are  but  very  few 
substances  which  expand  when  they  become  solid.  Iron 
is  such  a  substance,  and  it  is  owing  to  this  property  that  it 
is  so  well  adapted  for  castings.  As  it  solidifies,  it  expands 
so  as  completely  to  fill  the  mould.  Bismuth  expands  in 
the  same  way,  and  also  the  alloy  of  antimony,  lead,  and 
tin,  which  is  used  for  type-metal. 

This  irregular  expansion  of  water  is  of  the  greatest  im- 
portance. Before  freezing  it  begins  to  grow  lighter,  so  that 
the  freezing  begins  at  the  surface ;  and  the  ice,  being 
lighter  still  and  also  a  poor  conductor  of  heat,  floats  upon 
the  water  and  keeps  it  from  freezing  very  deep.  If  water 


244  HEAT. 

continued  to  contract  as  it  cooled,  it  would  begin  to  freeze 
at  the  bottom,  and  during  the  winter  our  lakes  and  rivers 
would  become  solid  masses  of  ice.  This  would  be  fatal  to 
all  animal  life  in  the  water ;  and,  as  water  is  a  very  poor 
conductor  of  heat,  it  would  melt  only  to  the  depth  of  a  few 
feet  during  the  summer. 

243.  Latent  Heat  of  Steam  and  Vapor.  —  Not  only  is  the 
latent  heat  of  water  greater  than  that  of  any  other  liquid, 
but  that  of  steam  and  watery  vapor  is  greater  than  that  of 
any  other  gas  or  vapor,  hydrogen  alone  excepted. 

244.  Heating  by  Steam.  —  It  is  now  quite  common  to 
warm    buildings    by  steam.     Pipes    run    from    the    boiler 
through    the  rooms  to  be  heated,  and    then  back  to  the 
boiler  again.     The  steam  passes  from  the  boiler  into  these 
pipes,  where  it  is  condensed  and  runs  back  as  water  to  the 
boiler.     Now  every  pound  of  water  converted  into  steam 
in  the  boiler  takes  up  over  900  units  of  heat,  and  every 
pound  of  steam  which  condenses  in  the  pipes  gives  out 
the  same  amount  of  heat  into  the  rooms.     The  water  is 
thus  made  to  act  as  carrier  of  heat  between  the  furnace 
and  the  room  where  it  is  wanted.     As  fast  as  it  gives  up 
the  heat  which  it  has  absorbed  from  the  furnace,  it  runs 
back  to  the  boiler  for  more. 


SUMMARY. 

The  high  specific  and  latent  heat  of  water  tends  to  make 
the  transition  from  winter  to  summer  and  from  summer  to 
winter  more  gradual.  (241.) 

The  irregular  expansion  and  contraction  of  water  when 
heated  and  cooled  prevents  the  lakes  and  rivers  from  freez- 
ing solid  in  the  winter.  (242.) 

Steam  has  a  high  specific  and  latent  heat,  which  becomes 
sensible  on  condensation.  It  is,  therefore,  used  for  heating 
buildings.  (243,  244.) 


HEAT.  245 


THERMAL   INSTRUMENTS. 

245.  The  Mercurial  Thermometer. — The  ordinary  ther- 
mometer is  one  of  the  most  important  thermal  instruments, 
and  is  used,  as  its  name  implies,  to  measure  temperature. 
It  consists  of  a  fine  glass  tube  with  a  bulb  blown  upon  one 
end  of  it.  At  the  ordinary  temperature  the  bulb  and  a 
part  of  the  tube  are  filled  with  mercury. 

In  order  to  fill  the  tube  with  mercury,  a  cup  of  glass  or 
india-rubber  is  connected  with  the  top  of  the  tube.  This 
cup  is  filled  with  mercury,  and  the  bulb  heated  so  as  to 
drive  out  a  part  of  the  air.  The  bulb  is  then  allowed  to 
cool,  and  a  part  of  the  mercury  falls  into  the  tube  to  take 
the  place  of  the  air  driven  out.  This  mercury  is  now 
boiled  a  short  time,  and  in  this  way  the  remainder  of  the 
air  is  expelled.  The  bulb  being  allowed  to  cool  again, 
more  mercury  passes  in  and  fills  both  bulb  and  tube.  The 
mercury  is  now  heated  up  to  the  highest  temperature  which 
the  thermometer  is  intended  to  measure,  and  the  end  of 
the  tube  is  sealed  air-tight  by  melting  the  glass.  As  the 
bulb  cools  again,  the  mercury  falls  in  the  tube,  leaving  a 
vacuum  above  it. 

The  next  thing  to  be  done  is  to  graduate  the  thermome- 
ter. On  the  thermometer  scale  there  are  two  fixed  points, 
—  that  at  which  ice  melts,  and  that  at  which  water  boils. 
These  are  called  i\\e  freezing-point  and  the  boiling-point. 

The  freezing-point  is  found  by  plunging  the  bulb  into 
melting  ice,  and  noting  the  position  of  the  mercury  in  the 
tube.  Melting  ice  is  used  rather  than  freezing  water,  be- 
cause it  is  found  that  if  water  be  kept  perfectly  still  it  can 
be  cooled  several  degrees  below  the  freezing-point  before 


246 


HEAT. 


it  congeals  ;  while  ice,  at  the  ordinary  pressure,  always 
melts  at  the  same  temperature. 

We  have  also  seen  that  the  boiling-point  of  water  is 
affected  by  various  circumstances.  Hence  the  boiling- 
point  of  the  scale  cannot  be  found  by  plunging  the  bulb 
into  boiling  water.  But  whatever  may  be  the  temperature 
at  which  water  boils,  its  steam  always  has  the  same  tem- 
perature at  the  ordinary  pressure.  The  boiling-point  is 
then  found  by  enclosing  the  bulb  and  tube  in  a  steam- 
bath,  as  shown  in  Figures  171  and  172. 

On  the  Fahrenheit  scale,  which  is  the  one  in  common 
use  in  this  country  and  England,  the  freezing-point  is 


Fig.  171. 


Fig.  172. 


marked  32,  and  the  boiling-point  212.  The  space  between 
the  two  is  consequently  divided  into  180  equal  parts.  The 
rise  of  temperature  corresponding  to  the  rise  of  the  mer- 
cury through  one  of  these  parts  is  called  one  degree.  The 


HEAT.  247 

equal  divisions  are  continued  above  the  boiling-point  and 
below  the  freezing-point.  The  scale,  however,  is  not  ex- 
tended below  — 38°  nor  above  576°,  since  mercury  freezes 
at  one  of  these  points  and  boils  at  the  other. 

On  the  Centigrade  scale,  which  is  the  one  commonly  used 
in  France,  the  freezing-point  is  marked  o,  and  the  boiling 
point  100.  5°  of  this  scale  correspond,  then,  to  9°  of  the 
Fahrenheit  scale. 

Since  the  Centigrade  scale  is  a  decimal  one,  it  has  been 
adopted  by  most  scientific  men  throughout  the  world. 

A  third  scale,  known  as  Reaumur's,  is  in  general  use  in 
Germany.  On  this  scale  the  freezing-point  is  marked  o, 
and  the  boiling-point  80. 

246.  The   Alcohol    Thermometer.  —  When    temperatures 
below  — 38°  are  to  be  measured,  alcohol  is  used  instead 
of  mercury.     An  alcohol  thermometer  is  not,  however,  so 
accurate  as  a  mercurial  one. 

247.  The  Air  Thermometer.  —  Mercury,  as  we  have  seen, 
cannot  be  used  to  measure  very  high  temperatures.     There 
are  various  ways  of  measuring  such  temperatures,  but  the 
best  is  by  means  of  the  air  thermometer.     The  expansive 
force  of  air  is  very  regular  for  all  known  temperatures,  but 
it  expands  so  rapidly  that  to  measure  the  ordinary  range  of 
temperatures  would  require  too  long  a  tube. 

The  expansion  of  the  air  in  the  tube  can  be  indicated 
by  the  movement  of  a  column  of  liquid  upon  which  it  acts. 

248.  The  Differential  Thermometer.  —  Leslie  constructed 
an  instrument  which  shows  the  difference  in  temperature 
between  two  neighboring  substances  or  places,  and  which 
is  hence  called  the  differential  thermometer.     In  this  instru- 
ment two  bulbs,  A  and  B,  filled  with  air,  are  connected  by 
means  of  a  bent  tube,  as  in  Figure  173.     A  little  colored 
liquid  fills  the  lower  part  of  this  tube,  and  rises  to  the 
levels  C  and  D  when  both  bulbs  are  of  the  same  tempera- 
ture.    But  should  A  become  warmer  than  B,  since  air 


248 


HEAT. 


Fig.    173- 


expands  very  much  for  an  increase  of  temperature,  the. 
column  of  liquid  will  be  pushed  down  at  C  and  made  to 
rise  at  D ;  and  this  motion  will  be 
reversed  when  B  becomes  warmer 
than^.  Such  an  instrument  will 
therefore  indicate  any  difference  of 
temperature  with  great  delicacy.  The 
liquid  in  the  tube  ought  to  be  one 
which  is  not  volatile.  Sulphuric  acid 
is  frequently  used. 

The  most  delicate  of  all  differential 
thermometers  is  the  thermo-electric 
pile,  which,  with  its  ..  accompanying 
galvanometer,  will  be  described  here- 
after (see  Electricity,  pages  265  and 
283). 

249.  Breguefs  Metallic  Thermometer.  —  This  instrument 
consists  of  a  spiral  (Figure  174)  composed  of  silver,  gold, 
and  platinum,  rolled  to-  Fi 

gether  so  as  to  form  a 
very  fine  ribbon.  In 
this  state  it  is  sensitive 
to  an  exceedingly  slight 
change  of  temperature, 
becoming  coiled  or  un- 
coiled, owing  to  the  dif- 
ferent expansion  of  the 
metals  of  which  the 
compound  ribbon  is 
made.  A  needle  at- 
tached to  one  extremi- 
ty of  the  coil  points  to 
a  scale  which  is  gradu- 
ated by  the  aid  of  an  ordinary  thermometer,  a  is  a  rod 
put  in  the  axis  of  the  spiral  to  keep  it  in  place. 


HEAT.  249 

250.  Effect  of  Temperature  upon  Measures  of  Time.  — 
The  rate  of  a  clock  depends  upon  the  time  in  which  its 
pendulum  vibrates,  and  that  of  a  watch  upon  the  time  of 
oscillation  of  its  balance-wheel.     Now  the  time  of  vibra- 
tion of  a  pendulum  depends  upon  its  length  ;  and  since 
the  change  of  temperature  alters  the  length  of  a  pendu- 
lum,   it  likewise  alters  its  time  of  vibration.     The  higher 
the  temperature,  the   longer  does  the  pendulum  become, 
and  the  more  slowly  does  it  vibrate.      In  like  manner  a 
change  of  temperature,  by  altering  the  dimensions  of  the 
balance-wheel  of  a  watch   and    the  force  of  the   spring, 
will  alter  its  time  of  oscillation  in  such  a  manner  that  it 
will  vibrate  more  slowly  in  hot  weather  than  in  cold. 

These  sources  of  error  may  be  obviated  by  means  of 
certain  compensations. 

251.  Graham's  Mercurial  Pendulum.  —  The  first  attempt 
to  compensate  for  change  of  length  in  a  pendulum  was 
made  by  Graham,  an  English  clockmaker.     The  rod  of 
his  pendulum,   Figure   175,  was  made  of  glass,     p. 

to  the  lower  end  of  which  was  attached  a  cylin- 
drical vessel  containing  mercury.  As  the  glass 
rod  expands  by  heat,  the  bottom  of  the  vessel 
which  contains  the  mercury  will  of  course  be 
rendered  more  distant  from  the  point  of  suspen- 
sion, but  since  the  column  of  mercury  resting  on 
this  base  expands  upwards,  its  centre  of  gravity 
is  raised,  or  brought  nearer  the  point  of  suspen- 
sion. The  lowering  of  the  centre  of  gravity,  due 
to  the  expansion  of  the  glass,  may  thus  be  coun- 
teracted by  the  rise  of  the  same,  due  to  the  ex- 
pansion of  the  mercury.  The  correction  for  im- 
perfect compensation  is  made  by  raising  or  lower- 
ing the  cylinder  of  mercury  by  means  of  a  screw. 

252.  Compensation  Balance-  Wheel.  —  If  the  bal- 
ance-wheel   of  a  chronometer   be  formed,  as  in 


250  HEAT. 

Figure  176,  not  with  one  continuous  rim,  but  with  a  broken 
rim  of  several  separate  pieces,  all  of  which  are  fixed  at  one 
end  and  free  at  the  other,  the  free  ends  being  loaded  ;  and 
further,  if  each  piece  be  composed  of  two  metals,  of  which 
the  most  expansible  is  placed  without ;  then  it  is  evident 
Fi  :  6  that  on  a  rise  of  temperature  the 

loaded  ends  will  approach  the  centre. 
This  may  be  so  arranged  as  to  coun- 
teract the  effect  produced  on  the  rate 
of  the  chronometer  by  the  expansion 
of  the  wheel,  which  carries  the  cir- 
cumference farther  from  the  centre. 

253.  Other  Effects  of  Expansion. 
—  It  requires  very  intense  pressure  to  produce  the  same 
change  of  volume  in  a  solid  or  liquid  body  as  that  which 
is  occasioned  by  a  very  small  change  of  temperature.  It 
follows  from  this  that  the  force  exerted  by  solids  in  con- 
tracting or  expanding,  or  by  liquids  in  expanding,  must  be 
very  great.  If  a  strong  vessel  be  entirely  filled  with  a 
liquid  and  then  sealed  tightly,  the  vessel  will  burst  if  there 
be  a  considerable  rise  of  temperature. 

In  like  manner  it  has  been  calculated,  that  a  bar  of 
wrought  iron  whose  temperature  is  15°  F.  above  that  of 
the  surrounding  medium,  if  tightly  secured  at  its  ex- 
tremities, will  draw  these  together,  with  a  force  of  one  ton 
for  each  square  inch  of  section,  on  cooling  down  to  the 
surrounding  temperature. 

In  the  arts  it  is  of  great  importance  to  bear  in  mind  the 
intensity  of  this  force,  sometimes  with  the  view  of  guarding 
against  its  action,  and  sometimes  in  order  to  make  it  useful. 
Thus,  bars  of  furnaces  must  not  be  fitted  tightly  at  their 
extremities,  but  must  at  least  be  free  at  one  end.  In 
making  railways,  also,  a  small  space  must  be  left  between 
the  successive  rails.  For  a  similar  reason  water-pipes  and 
gas-pipes  are  fitted  to  each  other  by  telescopic  joints. 


HEAT.  251 

As  an  instance  of  the  advantage  which  may  be  derived 
from  the  force  of  contraction,  we  may  mention  the  fa- 
miliar method  by  which  tires  are  secured  on  wheels.  The 
tire  is  put  on  hot,  when  it  fits  loosely,  but  as  it  cools  it 
contracts  and  grasps  the  wheel  with  very  great  force. 

254.  DanieWs  Dew-point  Hygrometer.  —  A  hygrometer  is 
an  instrument  for  measuring  the  amount  of  moisture  in  the 
air.     The  one  invented  by  Daniell  is  shown  in  Figure  177. 
It  is  composed  of  two  glass  bulbs.     The  bulb  A  is  more 
than   half  filled   with  ether,   and 

contains  a  delicate   thermometer  ^ 

plunged  in  the  ether ;  the  space 
above  is  void  of  air  and  of  every- 
thing but  the  vapor  of  ether.  The 
bulb  B  is  covered  with  some  fine 
fabric,  such  as  muslin,  upon  which 
ether  is  dropped  ;  the  evaporation 
of  the  ether  produces  intense  cold, 
in  consequence  of  which  the  ether 
vapor  inside  B  is  rapidly  con- 
densed, and  of  course  the  ether  in  A  as  rapidly  evaporates. 
The  evaporation  of  the  ether  at  A  cools  the  bulb  until  the 
air  in  contact  with  it  sinks  below  the  dew-point ;  that  is, 
the  temperature  at  which  the  moisture  in  the  air  begins  to 
be  deposited  as  dew.  The  bulb  A  is  made  of  black  glass 
in  order  that  this  deposition  may  be  more  readily  observed. 
At  the  moment  of  deposition  the  thermometer  in  A  is  read. 
When  the  dew  disappears,  as  the  temperature  rises,  the 
same  thermometer  is  also  read,  and  the  mean  of  these  two 
readings  is  taken  to  indicate  the  dew-point.  The  ther- 
mometer C  gives  the  temperature  of  the  air.  The  nearer 
the  dew-point  is  to  the  temperature  of  the  air,  the  nearer 
the  air  is  to  being  saturated  with  vapor. 

255.  Wet  and  Dry  Bulb  Hygrometer.  —  This  instrument 
was  devised  by  Mason,  and  consists  of  two  thermometers 


252 


HEAT. 


Fig.  178. 


(Figure  178)  placed  side  by  side,  one  having  a  dry  bulb 
and  the  other  a  bulb  covered  with  muslin,  kept  moist  by 

means  of  a  string  dipping  in 
water.  The  wet  bulb  is 
chilled  by  the  evaporation 
of  the  water  from  it,  since 
this  evaporation  renders 
some  of  its  heat  latent. 
The  drier  the  air,  the  more 
rapid  the  evaporation,  and 
the  greater  the  difference 
between  the  readings  of  the 
wet  and  dry  bulb  thermom- 
eters. 

When  we  speak  of  the  hu- 
midity of  the  air,  we  do  not 
mean  the  absolute  amount 
of  vapor  which  it  holds,  but 
the  degree  of  its  saturation. 
Thus,  a  cubic  foot  of  air  at 
32°  is  saturated  by  two 
grains  of  water ;  but  at  68° 
it  requires  7.5  grains  to  saturate  it.  When  the  air  is  com- 
pletely saturated,  its  humidity  is  said  to  be  100 ;  when 
half  saturated,  50;  when  three  fourths  saturated,  7 5 ;  and 
so  on. 

256.  Edsoris  Hygrodeik.  —  This  is  shown  in  Figure  179, 
and  is  an  improved  form  of  Mason's  hygrometer.  It  dif- 
fers from  all  other  hygrometers  in  having  a  dial,  over 
which  moves  a  pointer,  showing  at  a  glance  the  temper- 
ature, the  degree  of  humidity,  the  absolute  amount  of 
vapor  in  each  cubic  foot  of  air,  and  the  dew-point. 


253 


SUMMARY. 

One  of  the  most  important  thermal  instruments  is  the 
thermometer.  The  thermometer  scales  most  used  are  Fahren- 
heit's, the  Centigrade,  and  Reaumur's.  (245  -  247.) 

Breguefs  thermometer  indicates  changes  of  temperature 
by  the  unequal  expansion  of  metallic  ribbons.  (249.) 

The  differential  thermometer  serves  to  measure  the  dif- 
ference of  temperature  at  two  places.  The  most  delicate 
differential  thermometer  is  the  thermopile.  (248.) 

The  expansive  power  of  heat  may  be  made  to  regulate 
the  rate  of  clocks  and  watches.  (250-252.) 

The  hygrometer  is  an  instrument  for  measuring  the  amount 
of  moisture  in  the  air.  (254-256.) 


254  HEAT. 

CONCLUSION. 

There  are  two  kinds  of  heat,  luminous  and  obscure ; 
and  each  is  radiated,  reflected,  refracted,  dispersed,  ab- 
sorbed, and  polarized,  in  the  same  way  as  light.  They 
are  both  radiated  from  an  incandescent  body,  but  luminous 
heat  is  more  refrangible  than  obscure  heat.  As  the  tem- 
perature of  a  body  is  raised,  it  at  first  radiates  only  the  less 
refrangible  rays,  but  as  it  grows  hotter  it  begins  to  send  out 
more  and  more  refrangible  rays,  until  it  becomes  white-hot, 
when  it  emits  all  the  rays  of  the  spectrum.  At  the  same 
time  the  obscure  radiations  become  more  intense. 

The  ordinary  spectrum  is  made  up  of  a  luminous  portion, 
which  is  prolonged  at  one  end  by  an  obscure  chemical,  and 
at  the  other  by  an  obscure  thermal  portion.  Each  part 
is  crossed  by  blank  lines,  which,  being  equally  devoid  of 
luminous,  thermal,  and  chemical  power,  show  that  the  three 
kinds  of  radiations  are  essentially  the  same,  differing  only 
in  refrangibility,  or  in  the  rate  of  vibration.  The  periods 
of  these  vibrations  may  be  so  changed  that  the  obscure 
thermal  and  chemical  radiations  become  luminous,  as  in 
calorescence  and  fluorescence. 

Heat  originates  in  the  vibrations  of  the  molecules  of 
bodies,  and  is  transmitted  by  imparting  these  vibrations  to 
the  ether.  It  is  absorbed  when  these  vibrations  are  again 
taken  up  by  the  molecules  of  gross  matter.  As  the  mole- 
cules of  any  body  can  vibrate  only  in  certain  periods, 
a  body  can  radiate  or  absorb  only  certain  qualities  of  heat. 

The  heat  which  a  body  absorbs  raises  its  temperature, 
changes  its  state,  and  causes  it  to  expand.  It  is  also  com- 
municated from  molecule  to  molecule  by  conduction,  and,  in 
gases  and  liquids,  by  currents,  or  convection. 


IV. 


ELECTRICITY 


ELECTRI  CITY. 


MAGNETISM. 

257.  Magnets.  —  In  studying  Electricity  it  is  necessary  to 
know  a  few  things  about  magnets. 

Bring  one  end  of  an  ordinary  bar  magnet  into  contact 
with  a  pile  of  iron  tacks ;  on  removing  it,  a  number  of  the 
tacks  are  carried  away  with  it.  This  illustrates  one  of  the 
leading  characteristics  of  a  magnet ;  namely,  that  it  attracts 
iron.  The  force  residing  in  a  magnet  and  shown  by  its  at- 
tracting iron  is  called  magnetism. 

There  is  a  certain  iron  ore  which  has  the  power  of  at- 
tracting iron.  This  ore  seems  to  have  been  first  found 
near  Magnesia,  a  city  of  Asia  Minor.  Hence  the  name 
magnet.  Natural  magnets  are  called  loadstones  (more  prop- 
erly lodestones},  that  is,  stones  that  lead  or  draw  iron. 

258.  The  Power  of  a  Magnet  resides  chiefly  at  the  Ends. — 
If  a  small   iron  ball  is  fastened  to  a  string,  and  moved 
alongside  a  bar  magnet,  it  is  scarcely  attracted  at  the  mid- 
dle of  the  bar.     As  it  approaches  either  end  it  is  attracted 
more  and  more  strongly,  until  it  is  brought  near  the  end, 
where  attraction  is  found  much  the  strongest.     The  force 
of  a  magnet,'  then,  resides  chiefly  at  the  ends. 

Put  a  piece  of  stiff  drawing-paper  over  a  strong  magnetic 
bar,  and  strew  fine  iron-filings  over  it.  Not  only  is  the 
position  of  the  magnet  below  shown  on  the  paper,  but  the 

Q 


258  ELECTRICITY. 

particles  of  iron  arrange  themselves  in  lines  radiating  from 
the  poles.  These  lines  are  called  lines  of  magnetic  force,  or 
magnetic  curves. 

Fig.  180. 


259.   The  Forces  at  the  Opposite  Ends  of  a  Magnet  act  in 
Opposite  Directions.  —  Suspend  a  bar 

Ing.  iSi.  w  *     t  • 

*  magnet  by  a  string  so  that  it  can  turn 
freely.     Bring  one  end  of  a  bar  mag- 
net near  one  end  of  the  suspended 
magnet,  and  the  latter  is  drawn  to- 
8  wards  it.      Reverse  the  ends  of  the 


bar  magnet,  and  the  end  of  the  sus- 
pended magnet  is  repelled.  This  shows  that  the  forces  at 
the  ends  of  a  magnet  act  in  opposite  directions. 

260.  The  Poles  of  the  Magnet.  —  The  ends  of  the  magnet, 
where  the  opposite  forces  reside,  are  called  poles. 

When  a  bar  magnet  is  poised  so  that  it  can  move 
freely,  it  takes  a  nearly  north  and  south  direction.  One  of 
its  poles  will  always  point  to  the  north,  and  is  called  the 
north  pole.  The  opposite  pole  is  called  the  south  pole.  A 
bar  magnet  thus  poised  so  as  to  turn  freely  is  called  a 
magnetic  needle. 

261.  The  Earth  acts  like  a  Magnet.  —  If  a  small  needle 
which  is  free  to  move  in  a  horizontal  plane  is  placed  upon 
a  bar  magnet,  its  south  pole  will  always  point  towards  the 
north  pole  of  the  latter.     If  a  small  dipping  needle,  that  is,  a 


ELECTRICITY.  259 

needle  which  is  free  to  move  in  a  vertical  plane,  is  placed 
above  the  middle  of  a  bar  magnet,  it  stands  parallel  with 
the  bar  magnet.  If  it  is  moved  towards  the  north  pole 
of  the  magnet,  the  south  pole  begins  to  dip  towards  the 
magnet ;  and  the  farther  it  is  moved  towards  this  pole,  the 
more  it  dips.  If  it  is  moved  from  the  centre  of  the  bar 
magnet  towards  the  south  pole,  its  north  pole  dips  in  the 
same  way. 

We  have  already  seen  that  a  magnetic  needle  free  to 
move  in  a  horizontal  plane  points  north  and  south  when 
held  above  the  earth.  It  is  also  found  that  a  dipping 
needle  in  the  vicinity  of  the  equator  stands  parallel  with 
the  plane  of  the  horizon,  and  that,  when  carried  north  from 
the  equator,  its  north  pole  dips  towards  the  horizon ;  while, 
if  it  is  carried  south  from  the  equator,  its  south  pole  dips 
towards  the  horizon. 

It  is  thus  found  that  the  earth  acts  upon  a  magnetic 
needle  like  a  magnet  whose  poles  are  near  the  poles  of  the 
earth ;  its  south  pole  near  the  north  pole  of  the  earth,  and 
its  r  orth  pole  near  the  south  pole  of  the  earth. 

The  French  regard  the  magnetic  pole  of  the  earth  near 
the  north  pole  as  a  north  pole,  and  the  pole  of  the  magnetic 
needle  which  points  towards  this  pole  as  the  south  pole. 
The  pole  of  the  magnet,  therefore,  which  we  call  the  north 
pole,  the  French  call  the  south  pole,  and  vice  versa. 

262.  Like' Poles  of  Magnets  repel  and  unlike  Poles  attract. 
—  This  has  already  been  shown  by  the  action  of  a  bar  mag- 
net upon  a  dipping  needle.     It  may  be  further  shown  by 
bringing  the  north  pole  of  a  bar  magnet  near  the  north 
pole  of  a  needle,  which  will  be  repelled.     On  bringing 
the  south  pole   of  this  magnet   near  the   north   pole  of 
the  needle,  it  will  be  attracted. 

263.  Magnetism  is  developed  in  Iron  or  Steel  by  Induc- 
tion. —  When  a  piece  of  soft  iron  is  brought  into  contact 
with  the  pole  of  a  magnet,  it  will  attract  other  pieces  of 


200  ELECTRICITY. 

iron,  showing  that  magnetism  has  been  developed  in  the 
iron  by  contact  with  the  magnet.  Magnetism  can  be  de- 
veloped in  a  piece  of  steel  in  the  same  way.  The  iron 
however,  loses  its  magnetism  as  soon  as  it  is  taken  away 
from  the  magnet,  while  the  steel  retains  it.  It  is  not  neces- 
sary that  a  piece  of  iron  should  be  brought  into  actual 
contact  with  the  pole  of  a  magnet  in  order  that  magnetism 
may  be  developed  in  it,  but  merely  that  it  be  brought  very 
near  the  pole. 

Magnetism  developed  in  this  way  in  a  piece  of  iron  or 
steel  is  said  to  be  induced. 

264.  Forms  of  Magnets.  —  Ordinary  magnets  are  made 
Fig.  182.  °f  steel.     When  straight  they  are  called 

bar  magnets;  when  bent  into  the  shape  of 
the  letter  U  they  are  called  horseshoe  mag- 
nets. When  several  bar  or  horseshoe  mag- 
nets (see  Figure  182)  are  connected,  they 
constitute  a  magnetic  battery. 

265.  The  Making  of  Magnets.  —  Mag- 
nets are  often  made  by  contact  with  per- 
manent magnets  by  a  process  of  single 
or  double  touch.  In  the  former  case,  the 
steel  bar  to  be  magnetized  is  laid  on  a 
table,  and  the  pole  of  a  powerful  magnet  is  rubbed  from 
ten  to  twenty  times  along  its  length,  always  in  the  same 
direction.  If  the  magnetizing  pole  be  north,  the  end  of 
the  bar  it  first  touches  each  time  becomes  north,  and  the 
end  where  it  is  taken  off  becomes  south.  The  same  thing 
may  be  done  by  putting  one  pole  of  the  magnet,  say  the 
north,  first  on  the  middle  of  the  bar,  then  giving  it  a  few 
passes  from  the  middle  to  the  end,  returning  always  in  an 
arch  from  the  end  to  the  middle.  The  other  half  of  the 
bar  is  then  rubbed  in  the  same  way  with  the  south  pole  of 
the  magnet.  The  first  end  rubbed  becomes  the  south,  and 
the  other  the  north  pole  of  the  new  magnet. 


ELECTRICITY. 


26l 


Fig.  183. 


The  method  by  double  touch  is  shown  in  Figure  183.  The 
bar  s  n  to  be  magnetized  is  placed  on  a  piece  of  wood,  W, 
with  its  ends  resting 
on  the  extremities  of 
two  powerful  magnets 

NS  and   SN.     Two  ^_  _  -\\^rt'^ 

rubbing  magnets  are 
placed  with  their  poles 
near,  but  not  touch- 
ing, on  the  middle  of  sn,  inclined  to  it  at  an  angle  of  10° 
or  15°.  The  two  magnets  are  then  drawn  along  from  the 
middle  to  one  end  and  then  back  to  the  other,  and  so 
backwards  and  forwards  from  ten  to  twenty  times,  and 
lifted  from  the  magnetized  bar  again  at  the  middle.  Care 
must  be  taken  that  both  ends  are  rubbed  the  same  number 
of  times,  and  that  the  lower  poles  of  the  rubbing  magnets 
do  not  go  beyond  the  ends  of  the  bar.  Both  the  upper 
and  lower  surfaces  of  the  bar  must  be  rubbed  in  this  way, 
in  order  to  magnetize  it  fully.  A  small  piece  of  wood  may 
be  placed  between  the  poles  of  the  rubbing  magnets  to 

prevent  contact.  The  position 
of  the  poles  is  shown  in  the 
figure  by  the  letters  ;  JV  or  n 
meaning  a  north,  and  S  or  s  a 
south  pole. 

For  horseshoe  magnets  Hof- 
=//  fer's  method  is  generally  fol- 
lowed. The  inducing  magnet 
(see  Figure  184)  is  placed  vertically  on  the  magnet  to  be 
formed,  and  moved  from  the  ends  to  the  bend,  or  in  the  op- 
posite way,  and  brought  round  again  in  an  arch  to  the 
starting-point.  A  piece  of  soft  iron  is  placed  at  the  poles 
of  the  induced  magnet.  Both  magnets  should  be  of  the 
same  width. 


Fig.  184. 


262  ELECTRICITY. 


SUMMARY. 

Any  substance  which  will  attract  iron  is  called  a  magnet. 
The  force  which  enables  it  to  attract  iron  is  called  magnet- 
ism.  (257.) 

This  force  resides  chiefly  at  the  ends  of  a  magnet,  which 
are  called  its  poles.  It  radiates  from  these  poles  in  curved 
lines,  called  lines  of  magnetic  force,  or  magnetic  curves.  (258, 

2^0.) 

The  forces  residing  at  the  opposite  poles  of  a  magnet  act 
in  opposite  directions.  (259.) 

The  north  pole  of  a  dipping  needle  always  points  to- 
wards the  south  pole  of  a  bar  magnet,  when  held  over  it. 

The  earth  acts  upon  a  needle  like  a  magnet.  Its  mag- 
netic poles  are  situated  near  the  poles  of  its  axis.  As  we 
name  the  poles  of  a  magnet,  the  magnetic  pole  of  the  earth 
north  of  the  equator  is  a  south  pole,  and  the  one  south  of  the 
equator  is  a  north  pole.  The  French  call  the  magnetic  pole 
north  of  the  equator  a  north  pole,  and  the  end  of  the  nee- 
dle which  points  towards  it  a  south  pole.  (261.) 

Like  poles  of  magnets  repel,  and  unlike  poles  attract 
each  other.  (262.) 

A  magnet  can  develop  magnetism  in  iron  or  steel  by  in- 
duction. Soft  iron  loses  its  magnetism  as  soon  as  it  is  with- 
drawn from  the  influence  of  the  magnet,  while  steel  retains 
its  magnetism  permanently.  (263.) 

Ordinary  magnets  are  made  of  steel.  They  are  called, 
from  their  shape,  bar  magnets,  or  horseshoe  magnets.  (264.) 

Magnets  may  be  made  by  contact  with  other  magnets,  by 
a  process  of  single  or  double  touch.  (265.) 


ELECTRICITY. 


263 


Fig.  185. 


Zn 


NATURE  AND   SOURCES   OF   ELECTRICITY. 

VOLTAIC   ELECTRICITY. 

266.  The   Voltaic  Pair.  —  If  in   a  vessel  of  dilute  sul- 
phuric acid  we  suspend  a  plate  of  zinc  and   a  plate  of 
platinum  opposite  to  each  other,  and  not 

in  contact,  we  find  that  no  chemical  action 
whatever  takes  place,  provided  the  zinc 
and  the  acid  are  perfectly  pure.  As  soon, 
however,  as  the  plates  are  united  by  a  cop- 
per wire,  as  shown  in  Figure  185,  chem- 
ical action  begins.  Bubbles  of  hydrogen 
gas  rise  from  the  surface  of  the  platinum, 
and  the  zinc  slowly  dissolves,  zincic  sulphate  being  formed 
and  dissolved  in  the  liquid.  The  acid  does  not  act  at  all 
upon  the  platinum.  Such  an  arrangement  is  called  a 
voltaic  pair  or  cell. 

If  the  wire  connecting  the  plates  of  the  pair  be  held  over 
a  small  magnetic  needle  and  parallel  with  it,  the  needle 
turns  aside,  and  seeks  to  place  itself  at  right  angles  to  the 
wire,  showing  that  a  new  force  is  developed  in  the  wire. 
This  force  is  called  electricity. 

267.  The  Electric  Current.  —  If  the  vessel  just  used  be 
filled  with  dilute  muriatic  acid,  similar  effects  are  produced, 
except  that  we  get  zincic  chloride  instead  of  zincic  sulphate. 
"In  this  case  the  space  between  the  plates  is  filled  with 
molecules  consisting  of  hydrogen  and  chlorine  atoms,  as 
indicated  in  Figure  186,  where  we  have  at- 
tempted to  represent  by  symbols  a  single 

one  of  the  innumerable  lines  of  molecules 
which  we  may  conceive  of  as  uniting  the 
two  plates.  The  zinc  plate,  in  virtue  of 
the  Dowerful  affinity  of  zinc  for  chlorine, 


Fig.  1 86. 


264  ELECTRICITY. 

attracts  the  chlorine  atoms,  which  rush  towards  it  with 
immense  velocity ;  and  the  sudden  arrest  of  motion  which 
attends  the  union  of  the  chlorine  with  the  zinc  has  the 
effect  of  an  incessant  volley  of  atomic  shot  against  the 
face  of  the  plate.  Each  of  the  atomic  blows  must  give  an 
impulse  to  the  molecules  of  the  metal  itself,  which  will  be 
transmitted  from  molecule  to  molecule  through  the  material 
of  the  plate  and  the  connecting  wire,  in  the  same  way  that 
a  shock  is  transmitted  along  a  line  of  ivory  balls."  *  From 
the  fact  that  the  electric  motion  is  thus  transmitted  from 
molecule  to  molecule,  it  is  called  a  current.  It  must  be 
borne  in  mind,  however,  that  the  electric  current  is  not  a 
fluid  flowing  through  the  wire,  but  it  is  merely  "a  wire  or 
other  conductor  filled  with  innumerable  lines  of  oscillating 
molecules." 

But  these  very  impulses  which  impart  motion  to  the 
metallic  molecules  react  upon  the  liquid,  and  force  back 
the  hydrogen  atoms  towards  the  platinum  plate  ;  so  that, 
for  every  atom  of  chlorine  which  unites  with  the  zinc  plate, 
an  atom  of  hydrogen  is  set  free  at  the  platinum  plate. 
Thus  we  have  two  atomic  currents  in  the  same  liquid 
mass :  one  of  chlorine  atoms  setting  towards  the  zinc  plate, 
and  one  of  hydrogen  atoms  flowing  in  the  opposite  direc- 
tion towards  the  platinum  plate.  Corresponding  to  this 
motion  in  the  liquid  is  the  peculiar  atomic  motion  in  the 
metallic  conductor.  The  two  are  mutually  dependent. 
The  moment  the  connection  is  broken  so  that  the  motion 
can  no  longer  flow  through  the  conductor,  the  motion  in 
the  liquid  ceases.  We  know  nothing  of  the  mode  of  the 
molecular  motion  in  the  metallic  conductor.  It  is  appar- 
ently allied  to  heat,  but  is  capable  of  producing  very 
different  effects.  Since  we  are  ignorant  of  its  nature,  we 

*  First  Principles  of  Chemical  Philosophy,  by  Prof.  Josiah  P.  Cooke,  Jr.,  page 
121.  The  remainder  of  §  267,  together  with  §§  271  -  274,  is  mainly  condensed  from 
the  same  work. 


ELECTRICITY.  265 

cannot  be  sure  of  the  direction  in  which  the  current  flows. 
It  is  possible  that  there  may  be  a  double  current  in  the 
wire  as  well  as  in  the  liquid.  It  is  always  assumed,  how- 
ever, as  a  matter  of  convenience,  that  the  current  flows 
from  the  platinum  plate  through  the  wire  to  the  zinc,  and 
thence  back  through  the  liquid  to  the  platinum. 

268.  The  Galvanometer.  —  We  have  seen  that  the  elec- 
tric current  has  power  to  deflect  a  magnetic  needle.     If  the 
wire  is  wound  once  round  a  needle,  it  is  found  that  the 
deflection  is  greater  than  when  it  passes  merely  over  or 
under  it.     When  the  wire  is  wound  a  number  of  times 
around  the  needle  in  the  form  of  a  coil,  the  deflection  is 
greater  still.     In  this  case  we  get  virtually  as  many  cur- 
rents to  act  upon  the  needle  as  there  are  turns  in  the  coil. 
A  needle  placed  within  or  above  such  a  coil  gives  by  its 
deflection  a  ready  means  of  measuring  the  strength  of  the 
current.     Such  an  arrangement  is  called  a  galvanometer. 

269.  The  Astatic  Needle.  —  A  needle  may  be  rendered 
still  more  sensitive  to  the  action  of 

the  current  by  combining  it  with  a  Flg>  l87' 

second  needle  of  the  same  strength, 

with  its  poles  reversed.     The  second  J. 

.y  |i'  i ? 

needle  serves  to  neutralize  the  directive 

power  of  the  earth,  so  that  the  needles     ^==  ^s 

will  have  no  tendency  to  point  north 

and  south.     Such  a  combination  is  shown  in  Figure  187, 

and  is  called  an  astatic  needle  (from  a  Greek  word  meaning 

unsteady),  that  is,  one  having  no  directive  power. 

A  galvanometer  in  which  an  astatic  needle  is  used  is 
called  an  astatic  galvanometer.  One  needle  is  always  placed 
within  the  coil,  and  the  other  above  it. 

A  very  delicate  instrument  of  this  kind  is  shown  in  Fig- 
ure 1 88.  The  astatic  needle  is  placed  within  a  coil  of 
fine  copper  wire  carefully  insulated  with  silk,  and  is  sus- 
pended by  a  cocoon  thread  to  a  hook  supported  by  a  brass 

12 


266 


ELECTRICITY. 


Fig.  1 88. 


frame.  It  hangs  freely  without  touching  the  coil,  and  the 
upper  needle  moves  on  a  graduated  circle.  The  whole  is 

enclosed  in  a  glass  case,  and 
rests  on  a  stand  supported  by 
three  levelling-screws. 

When  the  direction  of  the 
current  is  changed,  the  needle 
of  the  galvanometer  turns  the 
opposite  way ;  hence  the  gal- 
vanometer serves  to  ascertain 
the  direction  of  the  current,  as 
well  as  its  strength. 

270.  Electrical  Conducting 
Power  or  Resistance.  —  Some 
materials  transmit  the  electric 

current  more  readily  than  others,  since  their  molecules 
yield  more  readily  to  this  peculiar  form  of  molecular 
motion. 

An  instrument  used  to  measure  the  relative  conducting 
power  of  different  substances  is  called  a  rheostat  (that  is, 
an  instrument  for  making  the  current  steady,  or  of  uniform 
strength).  Wheatstone's  rheostat  is  represented  in  Figure 
189.  It  is  constructed  so  as  to  introduce  into  or  withdraw 
from  the  circuit  a  considerable  amount  of  highly  resist- 
ing wire,  without  stopping  the  current.  If  consists  of 
two  cylinders,  one  of  brass,  the  other  of  well-dried  wood, 
turning  on  their  axes  by  a  crank.  The  wooden  cylinder 
has  a  spiral  groove  cut  into  it,  in  which  is  placed  a  fine 
metallic  wire  ;  the  brass  cylinder  is  smooth.  The  end  of 
the  wire  attached  to  the  wooden  cylinder  is  connected  by 
means  of  a  brass  ring  with  a  binding-screw  for  the  attach- 
ment of  a  battery  wire.  A  metallic  spring  pressing  against 
the  brass  cylinder  is  connected  with  the  other  binding- 
screw.  If  now  a  current  be  sent  through  the  wire,  it  will 
pass  through  all  that  portion  of  it  which  is  wound  at  the 


ELECTRICITY.  267 

time  upon  the  wooden  cyl- 
inder, but  it  will  not  pass 
through  the  portion  wound 
upon  the  brass  cylinder,  but 
through  the  cylinder  instead, 
since  the  latter  is  a  better 
conductor  than  the  fine  wire. 
The  wire  wound  upon  the 
brass,  then,  is  withdrawn 
from  the  circuit. 

When  the  rheostat  is  to 

be  used,  all  the  wire  is  wound  upon  the  wooden  cylinder, 
and  put  into  the  circuit  along  with  a  galvanometer.  If  now 
the  resistances  of  two  wires  are  to  be  tested,  the  galvan- 
ometer is  read  before  the  first  is  put  into  the  circuit. 
After  it  is  introduced,  the  needle  falls  back  in  consequence 
of  the  increased  resistance,  and  then  as  much  of  the  rheo- 
stat wire  is  withdrawn  from  the  circuit  as  will  bring  the 
needle  back  to  its  former  place.  The  quantity  thus  with- 
drawn is  shown  by  a  scale,  and  is  obviously  equal  in  re- 
sistance to  the  wire  introduced.  The  first  wire  is  then 
removed,  and  the  second  wire  is  tested  in  the  same  way  as 
the  first.  If  40  inches  were  withdrawn  in  the  first  case, 
and  60  inches  in  the  second,  the  resistance  offered  to  the 
current  by  the  first  wire  is  to  that  offered  by  the  second  as 
40  is  to  60 ;  or,  in  other  words,  the  former  is  two  thirds  of 
the  latter. 

By  means  of  the  rheostat  it  has  been  proved  that  the 
resistances  of  wires  of  the  same  material  and  of  uniform 
thickness  are  in  the  direct  ratio  of  their  lengths,  and  in  the 
inverse  ratio  of  the  squares  of  their  diameters.  Thus  a  wire 
of  a  certain  length  offers  twice  the  resistance  of  its  half, 
thrice  that  of  its  third,  and  so  forth.  Again,  wires  of  the 
same  metal,  whose  diameters  are  in  the  ratio  of  i,  2,  3, 
etc.,  offer  resistances  which  are  to  each  other  as  i,  £,  \, 


268  ELECTRICITY. 

etc.  Therefore,  the  longer  the  wire,  the  greater  the  resist- 
ance ;  the  thicker  the  wire,  the  less  the  resistance.  The 
same  holds  true  of  liquids,  but  not  with  the  same  exact- 
ness. The  following,  according  to  Becquerel,  are  the 
specific  resistances  of  some  of  the  more  common  substances, 
or  the  resistance  which  a  wire  of  each,  so  to  speak,  of  the 
same  dimensions,  offers  at  the  temperature  of  54°  F. :  — 
Copper,  i  ;  silver,  0.9  ;  gold,  1.4  ;  zinc,  3.7  ;  tin,  6.6  ;  iron, 
7.5  ;  lead,  n  ;  platinum,  11.3  ;  mercury  (at  57°),  50.7. 
For  liquids,  the  resistances  are  enormous  compared  with 
metals.  With  copper  at  32°  F.  as  i,  the  following  liquids 
stand  thus :  saturated  solution  of  blue  vitriol  at  48°, 
16,885,520  ;  ditto  of  common  salt  at  56°,  2,903,538  ;  white 
vitriol,  15,861,267  ;  sulphuric  acid,  diluted  to  TJT,  at  68°, 
1,032,020  ;  nitric  acid  at  55°,  976,000  ;  distilled  water  at 
59°,  6,754,208,000.  Gases  offer  even  greater  resistance  to 
the  current,  so  that  they  are  virtually  non-conductors. 

271.  Ohm's  Law.  —  The  force  of  the  current  must  de- 
pend upon  the  power  which  the  moving  atoms  exert  against 
the  zinc  plate.  The  effect  of  these  atomic  blows  must  be 
determined,  in  the  first  place,  by  the  chemical  force  which 
draws  the  atoms  towards  the  plate.  This  force  is  called 
the  electro-motive  force  of  the  voltaic  pair.  But,  in  the 
second  place,  each  moving  atom  is  but  one  of  a  long  line 
of  similar  atoms  which  it  drags  along  behind  it,  while  an 
equal  line  of  dissimilar  atoms  is  pushed  back  in  the 
opposite  direction.  These  lines  of  atoms  act  as  so  much 
dead  weight  to  resist  the  atomic  motion,  and  to  lessen  the 
effect  of  the  atomic  blows.  In  the  third  place,  each  line 
of  moving  molecules  in  the  liquid  is  connected  with  a  line 
of  vibrating  molecules  in  the  wire,  and  forms  with  it  a  con- 
tinuous chain  so  connected  that  the  amount  of  motion  must 
be  equal  at  all  points.  Thus  the  resistance  in  the  con- 
ducting wire  reacts  upon  the  whole  chain,  and  lessens  the 
effect  of  the  atomic  blows  upon  the  zinc  plate.  What  is 


ELECTRICITY.  269 

true  of  each  line  is  true  of  all  the  lines  in  the  electric  cur- 
rent. This  current  is  kept  up  by  the  chemical  activity  at 
the  zinc  plate.  This  activity  is  sustained  by  the  electro- 
motive force,  but  impeded  by  the  resistance  of  the  liquid 
and  the  wire.  Evidently  then  the  power  of  the  current  is 
directly  proportional  to  the  electro-motive  force  which  sustains 
the  motion,  and  inversely  proportional  to  the  sum  of  the  resist- 
ances throughout  the  circuit.  If  we  represent  the  power  of 
the  current  by  P,  the  electro-motive  force  by  E,  the  resist- 
ance in  the  conducting  wire  by  R,  and  the  resistance  in  the 
liquid  by  r,  we  shall  have 


The  principle  embodied  in  this  formula  is  known  as  Ohnts 
law. 

272.  Quantity  and  Intensity.  —  If  we  increase  the  size 
of  the  plates  in  the  voltaic  pair,  we  shall  increase  the  num- 
ber of  lines  of  moving  molecules  in  the  current.  When 
these  plates  are  connected  by  a  thick  metallic  conductor, 
so  that  there  shall  be  little  resistance  outside  the  liquid,  all 
the  lines  of  moving  molecules  will  be  excited  to  the  great- 
est activity  which  the  pair  can  give.  We  thus  obtain  a 
current  of  very  great  volume,  and  flowing  with  all  the  force 
which  a  single  pair  is  capable  of  maintaining.  The  mo- 
ment, however,  we  attempt  to  force  this  current  through  a 
great  length  of  wire,  we  interpose  a  resistance  to  the  atomic 
motion  which  tends  to  reduce  the  chemical  activity  ;  and 
as  this  resistance  must  increase  with  the  volume  of  the 
motion,  it  will  reduce  the  chemical  activity  to  what  it  would 
be  with  a  plate  of  much  smaller  size  and  giving  a  current 
of  much  less  volume.  By  increasing  the  size  of  the  plate, 
then,  we  increase  the  power  of  the  current  only  when 
there  is  little  resistance  outside  the  liquid.  We  thus  obtain 
a  current  composed  of  many  moving  lines  of  molecules,  — 


270  ELECTRICITY. 

that  is,  of  great  volume,  or  quantity,  but  the  molecular  mo- 
tion has  little  intensity,  or  power  of  overcoming  resist- 
ance. 

The  quantity  of  the  current,  then,  is  the  volume  of  the 
molecular  motion  ;  while  the  intensity  is  the  energy  of  this 
motion. 

It  is  evident  that  we  can  increase  the  intensity  of  the 
current  only  by  increasing  the  chemical  activity,  or  the 
electro-motive  force.  This  may  be  done  to  a  certain  ex- 
tent by  using  pairs  in  which  there  are  more  powerful 
affinities  between  the  plate  and  the  liquid.  The  electro- 
motive force  may,  however,  be  increased  to  almost  any 
extent  by  using  a  number  of  pairs,  and  connecting  them 

as  shown  in  Figure  190. 
The  platinum  plate  of  the 
first  cell  is  united  with  the 
zinc  of  the  second,  and  so 
on  to  the  last,  whose  plat- 
inum plate  is  united  with 

the  zinc  of  the  first.  Such  a  combination  is  called  a  gal- 
vanic or  voltaic  battery,  and  the  current  from  such  a  battery 
has  a  much  greater  power  of  overcoming  resistance  than 
that  from  any  single  cell,  however  large.  In  a  single  cell 
the  motion  throughout  any  single  line  of  molecules  is  sus- 
tained by  the  chemical  energy  at  only  one  point,  but  in  the 
battery  it  is  reinforced  at  several  points,  —  that  is,  at  every 
zinc  plate.  Where  before  we  had  a  single  atomic:"  blow, 
we  have  now  a  number  which  send  their  united  energy 
along  one  and  the  same  line.  The  electro-motive  force, 
then,  is  increased  in  proportion  to  the  number  of  cells; 
and  the  power  of  the  current  would  be  increased  in  the 
same  proportion,  were  it  not  for  the  fact  that  the  current 
has  to  traverse  a  greater  extent  of  liquid.  If  we  use  n 
cells,  both  the  electro-motive  force,  E,  and  the  liquid  re- 
sistance, r,  become  n  times  as  great,  while  the  resistance 


ELECTRICITY.  2  J  1 

in  the  wire,  R,  remains  the  same.     Ohm's  formula  then 

becomes 

n  E 


This  formula  shows  at  once  that  when  the  exterior  resist- 
ance, R,  is  little  or  nothing,  we  gain  little  or  nothing  by 

n  E  E 

increasing  the  number  of  cells,  for  —  is  equal  to  -.     If, 

on  the  contrary,  R  is  very  large,  there  is  great  gain  in  using 
a  number  of  cells,  for  we  increase  the  numerator  of  the 
fraction  much  more  rapidly  than  the  denominator. 

273.  The  Construction  of  Cells.  —  A  voltaic  pair  may  be 
constructed  of  any  two  metals,  provided  they  are  unequally 
acted  upon  by  the  liquid  used.  The  greater  the  difference 
in  this  respect,  the  better.  Practically,  sulphuric  acid  is 
found  to  be  the  best  liquid,  and  zinc  the  best  material  for 
the  active  plate. 

The  zinc  of  commerce,  however,  contains  impurities, 
which  give  rise  to  what  is  called  local  action,  and  cause  the 
zinc  to  dissolve  in  the  acid  when  the  battery  is  not  in 
action.  This  local  action  can  be  prevented  by  amalgamat- 
ing the  zinc,  that  is,  coating  its  surface  with  mercury. 
"  The  mercury  on  the  surface  of  the  zinc  plate  acts  as  a 
solvent,  and  gives  a  certain  freedom  of  motion  to  the  par- 
ticles of  the  metal.  These,  by  the  action  of  the  chemical 
process,  are  brought  to  the  surface  of  the  plate,  while  the 
impurities  are  forced  back  towards  the  interior,  so  that  the 
plate  constantly  exposes  a  surface  of  pure  zinc  to  the  action 
of  the  acid."  (See  Appendix,  Note  7.) 

In  the  second  place,  "the  hydrogen  gas,  which,  by  the 
action  of  the  current,  is  evolved  at  the  platinum  plate,  ad- 
heres strongly  to  its  surface,  and  with  its  powerful  affinities 
draws  back  the  lines  of  atoms  moving  towards  the  zinc 
plate,  and  thus  diminishes  the  effective  electro-motive  force. 
Moreover,  after  the  battery  has  been  working  for  some  time, 


272 


ELECTRICITY. 


Fig.  191. 


the  water  becomes  charged  with  zincic  sulphate  ;  and  then 
the  zinc,  following  the  course  of  the  hydrogen,  is  also  de- 
posited on  the  surface  of  the  platinum,  which  after  a  while 
becomes,  to  all  intents  and  purposes,  a  second  zinc  plate, 
and  then,  of  course,  the  electric  current  ceases." 

274.  Grove's  Cefi. —  Both  these  difficulties  are  overcome 

in  Groves  Cell,  shown  in  Figure  191. 
It  consists  of  a  hollow  cylinder  of  zinc 
immersed  in  a  vessel  of  dilute  sul- 
phuric acid.  Within  the  zinc  cylinder 
is  put  a  small  cylindrical  vessel  of 
porous  earthen-ware,  filled  with  the 
strongest  nitric  acid,  and  in  this  hangs 
the  platinum  plate.  "The  walls  of  the 
porous  cell  allow  both  the  hydrogen 
and  the  zinc  atoms  to  pass  freely 
on  their  way  to  the  platinum  plate,  but  the  moment  they 
reach  the  nitric  acid  they  are  oxidized,  and  thus  the  surface 
of  the  platinum  is  kept  clean,  and  the  cell  in  condition  to 
exert  its  maximum  electro-motive  power." 

275.  Bunseris  Cell.  —  If  in  Grove's 
cell  we  substitute  for  the  platinum  a 
plate  of  dense  coke,  such  as  forms  in 
the  interior  of  gas  retorts,  we  get  a 
very  much  cheaper  cell  of  nearly  equal 
power.     The  use  of  gas-coke  was  first 
suggested  by  Prof.   Bunsen,  and   this 
cell  is  therefore  called  Bunserfs  Cell. 
It  is  represented  in  Figure  192. 

276.  Danieirs   Cell.  —  This   cell   is 
shown  in  Figure  193.     The  outer  ves- 
sel is  of  copper,  and  serves  as  the  pas- 
sive plate.     Inside  this  is  a  vessel  of 

porous  earthen-ware,  containing  a  rod  of  zinc.  The  space 
between  the  copper  and  the  porous  cup  is  filled  with  a  solu- 


Fig.  192. 


ELECTRICITY. 


273 


Fig.  193. 


tion  of  blue  vitriol,  which  is  kept  saturated  by  crystals  of 
the  salt  lying  on  a  perforated  shelf.  The  porous  cup  is 
filled  with  dilute  sulphuric  acid.  The  porous  partition 
keeps  the  fluids  from  mingling,  but  does  not  hinder  the 
passage  of  the  current.  The  blue  vitriol 
which  is  in  contact  with  the  passive  plate 
serves  to  take  up  the  hydrogen.  There 
are  two  other  reasons  for  putting  the  sul- 
phuric acid  within  the  porous  cup  :  (i.)  if 
the  sulphuric  acid  came  in  contact  with 
the  copper,  it  would  tend  to  act  upon  it  as 
well  as  upon  the  zinc,  and  thus  to  diminish 
the  electro-motive  force;  (2.)  the  zincic  sul- 
phate formed  is  thus  kept  from  coming  in 
contact  with  the  copper.  If  it  were  allowed 
to  come  in  contact  with  the  copper,  it  would  be  decom- 
posed by  the  current  passing  through  the  cell,  and  zinc 
would  be  deposited  on  the  copper ;  and  both  plates  would 
soon  be  virtually  of  the  same  metal. 


Fig.  194. 


Fig.   195- 


Figure  194  shows  the  way  in  which  the  cells  of  a  bat. 
tery  are  connected  in  order  to  get  the  greatest  possible  in- 
tensity of  the  elect'ic  force ;  Figure  195  the  way  in  which 
they  are  connected  to  get  the  greatest  quantity.  In  the 
latter  case,  since  the  zincs  are  all  connected  together, 

12*  R 


274 


ELECTRICITY. 


-  X96-  they  form   virtually  one  large   plate ; 

and  the  same  is  true  of  the  plati- 
nums. When  considerable  intensity  as 
well  as  quantity  is  desired,  the  two 
forms  are  combined,  as  shown  in  Fig- 
ure 196. 

277.  Electrolysis.  —  If  two  strips  of 
platinum  be  hung  opposite  each  other 
in  a  cup  filled  with  muriatic  acid,  and 
one  of  them  be  connected  with  the  negative  pole  (that  is, 
the  zinc  end)  of  the  battery,  and  the  other  with  the  positive 
pole  (the  platinum  end),  the  muriatic  acid  will  be  decom- 
posed, the  hydrogen  passing  towards  the  negative  pole,  and 
the  chlorine  towards  the  positive  pole.  Here  are  two 
atomic  currents  flowing  in  opposite  directions,  just  as  in 
the  liquid  between  the  plates  in  the  voltaic  pair.  It  is 
found  to  be  true,  in  general,  that  when  any  compound 
liquid,  which  is  a  conductor  of  electricity,  is  introduced 
into  the  circuit,  it  is  similarly  decomposed.  This  decom- 
position of  a  substance  by  electricity  is  called  electrolysis. 
The  literal  meaning  of  the  word  is  loosening  by  electricity. 
The  substance  decomposed  by  the  electricity  is  called  the 
electrolyte.  The  metallic  conductors  through  which  the 
current  passes  into  and  out  of  the  electrolyte  are  called 
electrodes  (roads  of  electricity].  That  through  which  the 
electricity  passes  into  the  electrolyte  is  termed  the  anode 
(road  up],  and  that  through  which  the  current  passes  out  is 
termed  the  cathode  (road  down}.  The  electrolyte  is  always 
decomposed  into  two  parts,  one  of  which  appears  at  the 
anode  and  the  other  at  the  cathode.  The  former  is  called 
the  anion  (going  up,  or  to  the  anode) ;  the  latter,  the  cation 
(going  down,  or  to  the  cathode}. 

278.  The  Electrolysis  of  Cupric  Sulphate.  —  If  two  elec- 
trodes of  platinum  (Figure  197)  be  introduced  into  a  solu- 
tion of  cupric  sulphate  (blue  vitriol),  bubbles  of  gas  rise 


ELECTRICITY.  275 

from  the  anode.     This  gas  may  be  collected  by  filling  a 

test-tube  with  the  solution  of  cupric  sulphate, 

and  inverting  it  over  the  anode.     On  testing         Fis-  '97- 

the  gas,  we  find  it  to  be  oxygen.     On  remov- 

ing the  cathode  from  the  solution,  we  find  it 

to  be  coated  with  copper.     If  one  of  the  elec- 

trodes be  of  platinum  and  the  other  of  cop- 

per, and  the  platinum  be  made  the  anode, 

the  result  is  the  same.      If,  however,  the  cop- 

per be  made  the  anode,  the  cathode  is  still 

coated  with  copper,  but  no  gas  escapes  from  the  anode. 

The  most  probable  explanation  of  the  above  facts  is  as 
follows. 

The  electric  current  decomposes  the  cupric  sulphate  into 
copper  and  SO4.  This  action  may  be  expressed  by  an 
equation  thus  :  — 


Copper,  appearing  at  the  cathode,  is  the  cation  ;  and  SO4, 
appearing  at  the  anode,  is  the  anion. 

When  the  anode  is  platinum,  the  anion  acts  upon  the 
water  of  the  solution,  uniting  with  its  hydrogen  and  setting 
its  oxygen  free. 

H2O  +  SO4  =  H2  SO4  (sulphuric  acid)  +  O. 

So  that  the  escape  of  the  oxygen  gas  in  this  case  is  due  to 
a  secondary  action,  which  is  purely  chemical. 

.When  the  anode  is  of  copper,  the  anion,  instead  of  act- 
ing upon  the  water,  acts  upon  the  anode  itself. 

Cu  +  SO4  =  CuSO4. 

Hence  no  oxygen  escapes  in  this  case,  but  cupric  sulphate 
is  formed  as  rapidly  as  it  is  decomposed  ;  so  that  the  solu- 
tion always  remains  of  the  same  strength.  The  anode  is 
gradually  eaten  away  and  transferred  to  the  cathode. 


276  ELECTRICITY. 

When  any  compound  containing  a  metal  is  decomposed 
by  electricity,  the  metal  always  appears  at  the  cathode ; 
and  if  the  anode  is  of  the  same  metal,  the  solution  always 
remains  of  the  same  strength,  while  the  anode  is  gradually 
transferred  to  the  cathode. 

279.  The  Voltameter. — This  instrument  was  invented  by 
Faraday  for  testing  the  strength  of  a  current.  It  is  shown 
in  Figure  198.  Two  platinum  plates,  each  about  half  a 
square  inch  in  size,  are  placed  in  a  bottle  containing  water 
acidulated  with  sulphuric  acid ;  the  plates  are  soldered  to 
wires  which  pass  up  through  the  cork  of  the  bottle  and 
terminate  in  binding-screws  ;  a  glass  tube  fixed  into  the 
cork  serves  to  discharge  the  gas  formed  within.  When 
the  binding-screws  are  connected  with  the  poles  of  a  bat- 
tery, the  water  in  the 
bottle  begins  to  be  de- 
composed, and  hydrogen 
and  oxygen  are  set  free. 
If  now  the  outer  end  of 
the  discharging  tube  be 
placed  in  a  trough  of 
mercury,  and  a  small 
graduated  bell-glass,  like- 
wise filled  with  mercury, 
be  placed  over  it,  the 

mixed  gases  rise  into  the  bell-glass.     The  quantity  of  gas 
given  off  in  a  given  time  measures  the  strength  of  the  current. 

SUMMARY. 

The  electric  current  is  a  line  of  oscillating  molecules,  set 
in  motion  in  the  voltaic  cell  by  the  chemical  activity  at  the 
zinc  plate.  (258.) 

The  galvanometer  measures  the  strength  of  this  current ; 
and  the  rheostat,  the  resistance  of  the  conductor.  (259, 
261.) 


ELECTRICITY.  277 

The  power  of  the  current  equals  the  electro-motive  force 
divided  by  the  sum  of  the  resistances  throughout  the  cir- 
cuit. (271.) 

The  quantity  of  the  current  is  the  volume  of  the  molecu- 
lar motion  ;  its  intensity  is  the  energy  of  this  motion.  (272.) 

In  a  voltaic  cell  it  is  necessary  to  have  two  plates,  and  a 
liquid  which  acts  upon  one  more  strongly  than  upon  the 
other.  The  most  powerful  cells  are  Grove's  and  Bunseris. 


When  any  compound  liquid,  which  is  a  conductor  of 
electricity,  forms  a  part  of  the  circuit,  it  is  decomposed. 
This  decomposition  by  electricity  is  called  electrolysis.  It 
is  usually  attended  by  a  secondary  action,  which  is  purely 
chemical.  (277.) 

RELATIONS   OF  ELECTRICITY   TO   MAGNETISM. 

280.  The  Current  can  make  Iron  Magnetic.  If  a  part  of 
the  wire  of  the  circuit  be  wound  into  a  coil,  and  a  piece  of 
soft  iron  be  placed  inside  this  coil,  it  becomes  strongly 
magnetic  while  the  current  is  passing  ;  as  may  be  shown  by 
bringing  bits  of  iron  near  the  ends  of  the  iron  inside  the 
coil.  Such  a  magnet  is  called  an  electro-magnet..  The  coil 
is  called  a  helix.  If  the  coil  is  a  left-hand  coil  (see  Figure 
199),  the  end  at  which  the  current  enters  the  coil  will  be 

Fig.  199- 


found  by  means  of  the  magnetic  needle  to  be  the  north 
pole  ;  so  that,  by  reversing  the  current,  the  poles  of  the 
electro-magnet  will  be  reversed.  If  the  coil  is  a  right-hand 
one  (see  Figure  200),  the  end  at  which  the  current  enters 
is  found  to  be  the  south  pole. 


278 


ELECTRICITY. 
Fig.  200. 


When  the  current  is  broken,  the  soft  iron  instantly  loses 
its  magnetism,  and  the  bits  of  iron  no  longer  cling  to  it. 
If  a  steel  rod  is  used,  instead  of  a  soft  iron  one,  it  retains 
its  magnetism  after  the  current  is  broken.  If  the  wire  is 
wound  around  the  iron  in  several  layers,  the  strength  of  the 
magnet  is  greatly  increased. 

Fig.  20I.  The  strongest  electro-magnets  are 

of  the  horseshoe  form.  They  far  ex- 
ceed ordinary  magnets  in  power. 
Small  electro-magnets  have  been  made 
which  support  3500  times  their  own 
weight,  and  large  ones  which  hold  up 
a  weight  of  2500  pounds.  These 
magnets  are  much  stronger  when  pro- 
vided with  a  keeper,  or  armature,  that 
is,  a  piece  of  soft  iron  which  connects  the  two  poles,  as 
shown  in  Figure  201. 

281.  The  Wire  through  which  a  Current 
is  passing  is  a  Magnet.  —  If  the  current  be 
sent  through  a  coil  such  as  is  shown  in 
Figure  202,  and  the  end  of  a  rod  of  soft 
iron  be  brought  near  the  opening  in  the 
centre,  it  is  at  once  drawn  into  the  coil. 
Coils  have  been  constructed  powerful 
enough  to  draw  up  and  sustain  a  weight 
of  600  pounds. 

The  electric  current,  then,  not  only  de- 
velops magnetism  in  soft  iron,  but  the  coil 
itself,  through  whicli  the  current  is  pass- 
ing, is  magnetic.  Fine  iron-filings  will  ad- 


Fig.  202. 


ELECTRICITY.  279 

here  to  the  wire  which  joins  the  poles  of  a  battery,  show 
ing  that  any  wire  through  which  the  current  is  flowing  is 
magnetic. 

282.  Magneto-electricity.  —  We  have  now  seen  that  the 
electric  current  has  power  to  move  a  magnet. 

Excite  an  electro-magnet,  hang  the  rod  of  a  lifting-coil 
to  one  of  its  poles,  attach  the  lifting-coil  to  the  galvan- 
ometer, and  quickly  slip  it  over  the  rod,  which  is  now  a 
magnet.  The  needle  promptly  turns  aside,  but  soon  comes 
back  to  its  former  position.  Now  quickly  slip  the  coil  off 
from  the  rod,  and  the  needle  turns  in  the  opposite  direc- 
tion. 

This  experiment  shows  that  an  electric  current  is  de- 
veloped when  a  continuous  conductor  is  moved  near  a 
magnet.  A  current  thus  originated  by  a  magnet  is  said 
to  be  induced  by  it,  and  the  electric  force  thus  induced  is 
called  magneto-electricity. 

We  have  seen  that  the  electric  current  renders  a  piece 
of  soft  iron  placed  inside  a  helix  temporarily  magnetic. 

Attach  the  lifting-coil  to  the  galvanometer,  place  the  rod 
within  the  coil,  and  bring  it  quickly  in  contact  with  the 
pole  of  an  excited  electro-magnet.  Magnetism  is  devel- 
oped  in  the  rod,  and  a  current  in  the  wire  of  the  coil,  as 
is  shown  by  the  galvanometer.  The  needle  soon  returns 
to  its  former  position.  Now  quickly  detach  the  rod  and 
coil  from  the  magnet.  The  rod  loses  its  magnetism,  and  a 
current  is  developed  in  the  coil.  The  galvanometer  shows 
that  its  direction  is  the  opposite  of  that  of  the  former  cur- 
rent. 

It  appears,  then,  that  a  current  may  be  developed  in  a 
conductor  by  using  either  a  constant  or  a  variable  magnet. 
When  a  constant  magnet  is  used,  the  current  is  developed 
by  changing  the  relative  positions  of  the  rmgnet  and  the 
conductor  ;  when  a  variable  magnet  is  used,  by  changing 
the  strength  of  its  magnetism. 


280  ELECTRICITY. 


SUMMARY. 

The  wire  through  which  a  current  flows  is  magnetic. 

When  a  piece  of  soft  iron  is  placed  inside  a  helix,  and  a 
current  sent  through  the  wire,  magnetism  is  developed  in 
the  iron.  A  magnet  made  in  this  way  is  called  an  electro- 
magnet^ and  is  much  stronger  than  an  ordinary  magnet. 
(280,  281.) 

Electricity  can  be  developed  by  magnetism,  either  by 
moving  a  conductor  near  a  constant  magnet,  or  the  magnet 
near  the  conductor  ;  or  by  changing  the  strength  of  the 
magnetism  in  a  magnet  which  is  near  a  conductor. 

Electricity  developed  by  magnetism  is  called  magneto- 
electricity.  (282.) 

THE  RELATION  OF  ELECTRICITY  TO  HEAT. 

283.  Heat  developed  by  the  Current. — When  a  current 
passes  through  fine  wire,  an  intense  heat  is  produced,  suf- 
ficient in  some  cases  to  bring  it  to  a  white  heat,  and  even 
to  fuse  platinum  wire.  Experiments  upon 
the  heating  effects  of  the  current  may  be 
made  by  the  apparatus  shown  in  Figure  203. 
The  bottle  is  filled  with  alcohol,  which  is  a 
non-conductor.  The  thick  wires  n  and  /  are 
connected  with  a  battery,  and  within  the  bot- 
tle they  are  joined  with  a  fine  spiral  wire, 
surrounding  the  bulb  of  a  delicate  thermom- 
eter, /.  When  the  circuit  is  closed,  the  heat 
developed  is  communicated  to  the  alcohol, 
and  thus  to  the  thermometer.  It  is  found 
that  if  the  wire  be  kept  the  same,  or  of  the  same  resist- 
ance, the  heat  is  in  proportion  to  the  square  of  the  strength 
of  the  current.  Thus,  if  a  current  of  a  certain  strength 


ELECTRICITY.  28 1 

raises  the  thermometer  i°  in  a  minute,  a  current  of  twice 
the  strength  will  raise  it  4°  in  a  minute. 

Again,  if  by  means  of  a  rheostat  the  strength  of  the  cur- 
rent be  kept  at  the  same  point,  and  wires  of  different  resist- 
ance be  put  into  the  bottle,  the  heat  developed  is  in  pro- 
portion to  the  resistance  of  the  wire.  Thus,  if  with  a  wire 
of  a  certain  resistance  the  thermometer  be  raised  i°  per 
minute,  it  will  be  raised  2°  per  minute  with  a  wire  of  double 
the  resistance. 

Hence  the  heat  developed  in  a  conducting  wire  by  an  elec- 
tric current  is  proportional  to  the  square  of  the  strength  oj 
the  current,  and  to  the  resistance  offered  by  the  wire. 

A  very  pretty  illustration  of  the  fact  that  the  heat  is  pro- 
portional to  the  resistance  is  furnished  by  a  chain,  the 
alternate  links  of  which  are  made  of  silver  and  platinum. 
When  a  current  of  sufficient  strength  is  sent  through  the 
chain,  the  silver  links  remain  black,  while  the  platinum 
links  become  red  hot. 

284.  The  Voltaic  Arc.  —  When  the  ends  of  two  wires 
which  form  the  poles  of  a  powerful  battery  are  made  to 
touch,  and  then  are  separated  for  a  short  distance,  the 
current  does  not  cease  with  the  separation,  but  forces  its 
way  through  the  intervening  air,  with  an  intense  evolution 
of  light  and  heat.  The  heat  is  sufficient  to  melt  the  most 

o 

refractory  metals,  and  therefore  some  substance  rivalling 
the  metals  in  conducting  power,  but  much  more  infusible, 
must  be  found  to  act  as  the  poles  under  such  circumstan- 
ces. The  various  forms  of  carbon  are  well  suited  to  this 
purpose  ;  but  the  best,  both  for  conducting  power  and  dura- 
bility, is  the  coke  formed  in  the  retorts  in  the  distillation 
of  coal-gas.  Figure  204  represents  a  simple  arrangement 
for  producing  the  electric  light.  The  carbon  points.  P,  N, 
are  fixed  into  hollow  brass  rods,  which  slide  in  the  heads 
of  the  glass  pillars,  A,  A,  and  are  connected  with  the  bat- 
tery by  binding-screws,  s,  s.  The  points  are  made  to 


282  ELECTRICITY. 

touch,  and    the    current    is    sent  through    the    rods  ;  the 
points  are  then  separated  a  little,    when  a  light  appears 

Fig.  204. 


between  them  rivalling  that  of  the  sun  in  purity  and  splen- 
dor. On  examination  this  light  is  found  to  arise  chiefly 
from  the  intense  whiteness  of  the  tips  of  the  carbon  points, 
and  partially  from  an  arch  of  flame  extending  from  one  to 
the  other.  The  positive  pole  is  the  brighter  and  hotter, 
as  is  shown  by  the  fact  that,  on  intercepting  the  current,  it 
continues  to  glow  for  some  time  after  the  negative  pole  has 
become  dark. 

While  the  light  is  kept  up,  a  visible  change  takes  place 
in  the  condition  of  the  poles.  The  positive  pole  suffers  a 
loss  of  matter;  particles  of  carbon  pass  from  it  to  the 
negative  pole,  some  reaching  it,  and  some  being  burned  by 
the  oxygen  of  the  air  on  the  way.  There  is  a  similar  loss, 
though  to  a  much  less  extent,  at  the  negative  pole.  The 
positive  pole  becomes  hollowed  or  blunted,  and  the  nega- 
tive remains  pointed. 

The  heat  of  this  arch  of  flame,  or  voltaic  arc,  as  it  is 
called,  is  the  most  intense  that  can  be  produced,  and  is 
due  to  the  great  resistance  the  current  meets  in  traversin  \ 
the  air.  Platinum  melts  in  it  like  wax  in  the  flame  of  a 
candle.  Quartz,  the  sapphire,  magnesia,  lime,  and  other 
substances  equally  refractory,  are  readily  fused  by  it.  The 
diamond  becomes  white  hot,  swells  up,  fuses,  and  is  re- 
duced to  a  black  mass  resembling  coke. 

The  electric  light  is  caused,  not  by  the  combustion  of 


ELECTRICITY. 


Fig.  205. 


the  carbon,  but  by  its  incandescence.  The  light  can  con- 
sequently be  produced  in  a  vacuum,  and  below  the  surface 
of  water,  oils,  and  other  non-conducting  liquids.  It  is  thus 
quite  independent  of  the  action  of  the  air. 

With  a  battery  of  some  fifty  Bunsen's  cells,  a  light  is 
produced  of  very  great  brilliancy  ;  but  when  very  great 
power  is  to  be  obtained,  twice  or  thrice  that  number  must 
be  employed. 

285.  Thermo-electricity.  —  When  the  point  of 
junction  of  any  two  metals  is  heated,  a  current 
is  always  produced.     When  a  bar  of  antimony, 
A,  is  soldered  to  a  bar  of  bismuth,  B  (see  Fig- 
ure  205),   and  their  free  ends   are  connected 
with  a  galvanometer,  G,  a  current  passes  from 
the  bismuth  to  the  antimony  when  the  junction 
is  heated.     When  »S  is  cooled  by  applying  ice, 
or  otherwise,  a  current  in  the  opposite  direction 
is  produced.     Such  a  combination  of  metals  is 
called  a  thermo-electric  pair.     The  electricity  so 
developed  is  called  thermo-electricity  (heat  electricity). 

Metals  like  antimony  and  bismuth,  which  have  a  crystal- 
line structure,  are  best  suited  for  a  thermo-electric  pair. 

Farmer's  alloy  (of  zinc  and  antimony)  forms  a  much 
more  powerful  pair  with  bismuth  than  antimony  itself  does. 

286.  Thermo-eltctric    Battery.  —  One 
bismuth-antimony    pair    has    very    little 
power.     To   obtain  a  stronger  current, 
several   pairs  are  united,   as    shown    in 
Figure    206.      The    heat    in    this   case 
must  be  applied  only  to  one  row  of  sol- 
dered faces.      The  strength  of  the  cur- 
rent depends  on  the  difference  of  tem- 
perature of  the  two   sides  ;   and   to   in- 
crease it  to  the  maximum  the  one  series 
must  be  kept  in  ice  or  in  a  freezing  mix- 


Fig.  206. 


284  ELECTRICITY. 

ture,  whilst  the  other  is  exposed  to  an  intense  heat.  As 
in  the  galvanic  battery,  the  electric  force  is  proportionate 
to  the  number  of  pairs.  At  best,  however,  it  is  small,  and 
the  galvanometer  used  to  measure  it  must  be  a  very  deli- 
cate one. 

When  a  great  many  pairs  are  formed  into  a  battery,  they 
are  usually  arranged  as  shown  in  Figure  207,  which  repre- 
sents one  of  thirty  pairs.     The  odd 

Fig.  207. 

laces,  i,  3,  5,  etc.,  are  exposed  on 
one  side,  and  the  even  faces,  2,  4,  6, 
etc.,  on  the  other.  The  terminal 
bars  are  connected  with  the  bind- 
ing-screws. The  interstices  of  the 
bars  are  filled  with  gypsum  to  keep 
them  separate,  and  the  whole  is  put 
in  a  frame  of  non-conducting  material. 

Such  a  battery,  in  connection  with  a  sensitive  galvan- 
ometer, forms  the  most  delicate  differential  thermometer 
(248)  which  has  yet  been  constructed.  So  long  as  the 
opposite  faces  are  exposed  to  the  same  temperature,  no 
current  is  produced  ;  but  if  the  temperature  of  one  side 
becomes  higher  than  that  of  the  other,  a  current  is  at  once 
indicated.  If  the  hand,  for  instance,  be  brought  near  one 
side,  the  needle  shows  a  current ;  or  if  a  piece  of  ice  be 
held  near,  a  current  is  also  shown,  but  moving  in  the  op- 
posite direction. 

SUMMARY. 

When  the  current  passes  through  a  conductor,  heat  is 
developed.  The  heat  is  proportional  to  the  square  of  the 
strength  of  the  current,  and  to  the  resistance  offered  by  the 
conductor.  (283.) 

Advantage  is  taken  of  the  same  fact  in  the  development 
of  the  electric  light.  (284.) 


ELECTRICITY.  285 

Heat  has  power  to  develop  electricity  in  a  combination 
of  different  metals.  Electricity  thus  generated  is  called 
thermo-electricity.  (285.) 

The  thermo-electric  pile  is  a  very  sensitive  differential 
thermometer,  since  a  current  is  developed  by  the  slightest 
difference  of  temperature  between  the  two  faces.  (286.) 


FRICTIONAL   ELECTRICITY. 

287.  Electricity  developed  by   Friction.  —  When    a   cat's 
back  is  stroked  on  a  cold,  dry  day,  in  a  darkened  room, 
sparks  are  obtained  which  at  once  indicate  the  develop- 
ment of  electricity.     If  a  well-dried  rod  of  glass  or  gutta- 
percha  be  rubbed  with  a  piece  of  siik  or  flannel,  similar 
sparks  appear.      Hence  electricity  may  be  developed  by 
friction.     Such  electricity  is  called  frictional  electricity.     It 
is  found  by  experiment  that,  when  any  two  dissimilar  bodies 
are  rubbed  together,  electricity  is  developed  ;  but  when  the 
substances  are  conductors  of  electricity,  the  force  thus  de- 
veloped passes  off  silently  through  the  hands  and  body. 
In  order  to  detect  it,  the  substances  rubbed  together  must 
be  held  by  insulating  handles,  that  is,  handles  which  do 
not  conduct  electricity. 

288.  The  Electrical  Machine.  —  An  apparatus  for  gener- 
ating frictional   electricity  is  called  an  electrical  machine. 
The  one  shown  in  Figure  208  consists  of  a  thick  plate  of 
glass  turned  by  a  crank.     At  one   end  there  is   a  glass 
standard  surmounted  by  a  brass  ball.     From  this  standard 
project  two  brass  strips  in  the  form  of  a  clamp,  which  hold 
the  rubbers  against  the  glass  plate.     These  rubbers   are 
pieces  of  wash-leather  or  woollen  cloth,  covered  with  an 
amalgam  of  mercury,  lead,  and  tin.     At  the  opposite  end, 
on  a  glass  support,  is  a  long  cylinder  of  brass  with  rounded 
ends.     This  cylinder  is   the  prime  or  positive  conductor. 
The  brass  ball  connected  with  the  rubber  is  the  negative 


286  ELECTRICITY. 

conductor.      The   plate   and    conductors  of   the  machine 
must  be  well  insulated.     In  dry  and  frosty  weather  glass 

Fig.  208. 


insulates  very  well ;  at  all  other  times  it  becomes  covered 
with  a  scarcely  visible  layer  of  moisture,  which  very  much 
impairs  its  insulating  power.  The  deposition  of  moisture 
is  greatly  lessened  by  coating  the  glass  with  shellac. 

289.  Quantity  and  Intensity  of  Frictional  Electricity.  — 
With  a  medium-sized  electrical  machine  of  this  kind,  sparks 
are  readily  obtained  two  inches  long  by  presenting  a  con- 
ducting substance  to  the  ball  of  the  prime  conductor. 
Very  large  machines  will  give  a  spark  two  feet  in  length. 
Frictional  electricity,  then,  must  have  great  intensity,  in 
order  to  traverse  so  great  a  distance  of  a  non-conducting 
substance  like  the  air.  Its  quantity,  on  the  other  hand,  is 
next  to  nothing.  This  is  shown  by  connecting  the  positive 
conductor  with  one  end  of  the  wire  of  a  moderately  delicate 
galvanometer,  and  the  negative  conductor  with  the  other 
end,  and  working  the  machine.  The  needle  will  be  de- 
flected only  one  or  two  degrees.  The  great  tension  (or 
intensity)  and  the  small  quantity  of  friction il  electricity 
place  it  in  striking  contrast  with  voltaic  electricity. 


ELECTRICITY.  287 

The  positive  conductor  of  an  electrical  machine  answers 
to  the  positive  pole  of  a  galvanic  battery,  and  the  negative 
conductor  to  the  negative  pole,  and  the  friction  on  the 
plates  to  the  chemical  action  in  the  cells.  With  the  gal- 
vanic battery  an  enormous  quantity  of  electricity  is  obtained 
of  slight  tension  ;  with  the  electrical  machine,  a  small 
quantity  of  enormous  tension. 

290.  The  Electroscope,  —  If  a  pith  ball  hung  by  a  silk 
thread  from  a  glass  rod  be  brought  near  the  ball  of  a  prime 
conductor,  it  is  at  first  attracted  and  then  repelled.  This 
power  of  attracting  light  bodies  is  one  of  the  most  striking 
features  of  friclional  electricity.  It  grows  out  of  its  high  ten- 
sion, and  it  furnishes  the  most  ready  means  of  detecting  the 
presence  of  this  electricity,  as  the  needle  furnishes  the  most 
ready  means  of  detecting  the  presence  of  voltaic  electricity. 

An  instrument  constructed  on  this  principle 

Fig.  209. 

for   the    detection    of   frictional  electricity  is 
called  an  electroscope. 

The  pith-ball  electroscope  (Figure  209)  consists 
of  a  brass  conducting-rod  supporting  a  gradu- 
ated semicircle,  in  the  centre  of  which  is  a 
movable  index  made  of  very  light  wood,  with 
a  pith  ball  at  the  end.  When  it  is  attached  to 
the  prime  conductor  of  the  machine,  the  pith 
ball  is  repelled  as  soon  as  the  plate  is  turned. 

Fi,  ria  The  gold-leaf  electroscope  (Figure    210)   is  a 

more  delicate  instrument.  It  consists  of  a  hollow 
glass  ball,  the  neck  of  which  is  covered  by  a 
brass  cap.  Through  this  cap,  but  insulated  from 
it,  passes  a  brass  rod  having  a  brass  ball  at  its 
upper  end  and  two  narrow  strips  of  gold-leaf 
suspended  from  its  lower  end.  If  the  brass 
ball  be  brought  near  a  body  charged  with  elec- 
tricity, the  strips  of  gold-leaf  repel  each  other, 
as  in  the  figure. 


288  ELECTRICITY. 

291.  The  Electrical  Forces  on  the  Positive  ana  Negativt 
Conductors  act  in  Opposite  Directions.  —  Insulate  both  con- 
ductors of  the  machine,  and  charge  them  with  electricity 
by  turning  the  plate.     Bring  a  pith  ball  suspended  by  a  silk 
thread  in  contact  with   the  positive  conductor,  and  it  is 
soon  repelled.     Take  it  now  to  the  negative  conductor, 
and  it  is  strongly  attracted.     Discharge  now  the  pith  ball 
by  taking  it  in  the  hand,  and  again  bring  it  in  contact  with 
the  negative  conductor,  and  it  is  repelled  ;  but  on  taking  it 
to  the  positive  conductor  it  is  attracted.     We  see  then  that 
a  ball  which  is  repelled  by  the  force  on  one  conductor  is 
attracted  by  the  force  on  the  other.     In  other  words,  the 
forces  on  the  two  conductors  act  in  opposite  directions. 

These  opposite  electrical  forces  are  called  positive  and 
negative  forces. 

292.  Both  Electrical  Forces  are  always  developed  together. 
—  It  is  found  to  be  impossible  to  develop  one  of  these 
forces  without  at   the  same  time  developing   both.     The 
positive  force  always  appears  upon  one  of  the  substances 
rubbed  together,  and  the  negative  force  always    appears 
upon  the  other.     The  force  that  acts  in  the  same  way  as 
that  upon  the  prime  conductor  of  an  ordinary  electrical 
machine  is  called  positive  electricity ',  and  the  opposite  force 
is  called  negative  electricity.     Of  course,  in  order  that  both 
*he   forces   should  be   detected,  both   of  the   substances 
rubbed  together  must  be  insulated. 

293.  Induction.  —  If  an  insulated  copper  ball  be  connect- 

ed with  the  prime  conductor  of  the 

Fig.   211. 

machine,  and  a  small  insulated  con- 
C  .,  -j)  \J  ductor  be  placed  near  it  (see  Figure 

°  °  ^  °  211),  on  developing  electricity  and 

examining  the  condition  of  the  insu- 
lated  conductor,  opposite  electrical 
forces  will  be  found  to  be  developed 

upon  its  ends.     On  the  end  next  the  ball,  negative  force 


ELECTRICITY.  289 

will  be  found  ;  on  the  end  farthest  from  the  ball,  positive 
force. 

This  action  of  a  charged  body  upon  a  body  near  it  is 
called  induction.  The  insulated  conductor  is  said  to  be 
Polarized. 

When  an  insulated  conductor  is  brought  near  a  charged 
body,  it  is  first  polarized,  and  the  nearer  it  is  brought,  the 
higher  the  polarization  rises.  If  the  conductor  is  so  situ- 
ated that  it  can  discharge  its  force  at  the  end  nearest  the 
polarizing  body,  it  becomes  charged  with  the  same  electric 
force  as  the  polarizing  body  ;  if  it  discharges  from  the  op- 
posite end,  it  becomes  charged  with  the  force  opposite  to 
that  on  the  polarizing  body.  If  the  conductor  is  so  situ- 
ated that  it  can  discharge  quite  readily  at  both  ends,  but 
more  readily  at  one  end  than  at  the  other,  there  will  be 
three  steps  in  the  process.  It  will  first  become  polarized, 
then  charged,  and  finally  neutralized. 

If  the  conductor  can  discharge  quite  readily,  and  with 
equal  readiness  at  each  end,  there  will  be  only  two  steps 
in  the  process  :  it  will  be  first  polarized,  and  then  neutral- 
ized. 

294.  The  Polarization  of  the  Insulated  Conductor  depends 
on  the  Non- Conducting  Medium  which  separates  it  from  the 
Charged  Body.  —  Charge  a  metallic  disc,  and  bring  it  near 
the  ball  of  the  gold-leaf  electroscope  ;  the  leaves  diverge, 
owing  to  the  electricity  induced  upon  them.     Put  a  thick 
cake  of  shellac  between  the   disc  and   the  ball,   and  the 
leaves  diverge  still  more,  showing  that  the  polarization  has 
risen  higher.     The  polarization  of  a  body  changes  when- 
ever a  different  non-conductor  occupies  the  space  between 
it  and  the  charged  body.     The  polarized  condition  of  a 
body    then    depends    upon    the    non-conducting   medium 
which  separates  it  from  the  charged  body. 

295.  The  Charge  on  a  Solid  Insulated  Conductor  is  always 
on  the  Surface.  —  To  an  insulated  copper  ball  are  care- 

13  s 


2QO  ELECTRICITY. 

fully  fitted  two  hemispherical  metallic  caps  provided  with 
insulating  handles.  The  caps  are  placed  upon  the  ball, 
and  the  whole  apparatus  is  charged.  The  caps  are  then 
removed  and  examined,  and  are  found  to  be  charged,  while 
not  the  slightest  trace  of  a  charge  is  found  on  the  ball. 

296.  Distribution  of  the  Charge  on   the  Surface.  —  It  is 
found  by  experiment  that,  when  a  spherical  conductor  is 
charged  and  placed  in  the  centre  of  a  room,  the  charge  is 
distributed  uniformly  over  its  surface  ;  and  that,  when  an 
oblong  conductor  is  charged  and  placed  in  a  similar  situa- 
tion, the  charge  accumulates  at  the  ends. 

297.  The  Charge  which    any  Body  can    receive  depends 
upon  its  Facilities  for  carrying  on  Polarization.  —  This  fact 
is   illustrated   by  a  simple  piece  of  apparatus.      It  con- 
sists of  three  cups  made  to  fit  closely  within  one  another. 
The  outer  and  inner  ones  are   of   tin ;    the  middle  one, 
which  is  higher  than  the  others,  is  of  glass.      In  the  centre 
of  the  inside  tin  cup  there  is  an  upright  glass  tube,  within 
which  is  a  brass  chain  attached  to  the  bottom  of  the  cup, 
and  having  a  brass  ball  at  the   other  end.     Remove  the 
outside  tin  cup,  place  the  glass  cup  on  an  insulating  stand, 
and  bring  the  brass  ball  of  the  inner  cup  near  the  prime 
conductor  of  the  machine.      Few  sparks  will  pass,  showing 
that  the  cup  receives  but  a  small  charge.     Discharge  the 
cup,  replace  the  outside   tin  cup,  connect  the  latter  with 
one  of  the  conductors  of  the  machine,  and  bring  the  ball 
of  the  inside  cup  near  the  other  conductor  of  the  machine. 
A  large  number  of  sparks  can  now  be  made  to  pass,  show- 
ing that  the  cup  can   receive   a  much  larger  charge.     In 
the  first  case  polarization  has  to  be  carried  on  through  the 
glass  and  the  air  outside,  to  the  nearest  conductors  ;  while, 
in  the  second  case,  it  is  carried  on   merely  through  the 
glass  which  separates  the  two  coats.     Hence  there  is  much 
less  resistance  to  polarization  in  the  second  case ;  and,  as 
we  have  seen,  the  cup  receives  much  the  greater  charge. 


ELECTRICITY.  291 

Remove  the  inner  cup  by  taking  hold  of  the  glass  tube, 
and  then  the  glass  cup.  Very  little  electricity  will  be 
found  on  the  tin  cups,  but  on  rubbing  the  hand  over  the 
glass  cup  we  find  that  cup  to  be  charged. 

298.  The  Ley  den  Jar.  —  Replace  the  two  metallic  cups 
with  tinfoil,  and  the  apparatus  just  described  becomes  a 
Ley  den  jar.     This  jar  is  charged  by  connecting  its  outer 
coating  with  one  conductor  of  an  electrical  machine,  and 
the  inner  coating  with  the  other,  and  developing  electricity. 

The  jar  may  be  discharged  by  means  of  the  discharger, 
which  consists  of  two  bent  brass  arms  connected  by  a 
movable  joint  and  having  brass  balls  at  their  ends.  It  is 
fastened  at  the  joint  to  a  glass  handle.  To  discharge  the 
jar,  hold  the  discharger  by  the  glass  handle,  and  bring  one 
ball  in  contact  with  the  outer  coating  and  the  other  ball 
near  the  knob  connected  with  the  inner  coating. 

299.  The  Ley  den  Battery.  —  The  amount  of  charge  which 
a  Leyden  jar  can  receive,  other  things  being  equal,   evi- 
dently increases  with  the  size  of  the  coatings.     The  area 
of  the  coatings  can  be  increased,  either  by  making  the  jar 
larger,  or  by  connecting  together  several  smaller  jars.     The 
latter  arrangement  constitutes  a  Leyden  battery.     Like  the 
cells  of  the  voltaic  battery,   the  jars  can   be  connected  in 
two  ways  :  (i.)  the  outer  coating  of  one  may  be  connected 
with  the  inner  coating  of  the  next,  and  so  on  throughout 
the   series  ;    or,   (2.)   the   outer  coatings   may  all  be  con- 
nected together,  and  also  the  inner  coatings.     In  the  first 
case,  the  battery  is  discharged  by  bringing  the  inner  coat- 
ing of  the  first  jar  in  contact  with  the  outer  coating  of  the 
last ,  in  the  second  case,  by  bringing  the  connected  outer 
coatings    in    contact   with    the    connected    inner  coatings. 
Like    the   voltaic    battery,    when     the     Leyden    battery  is 
arranged  in  the  first  way,  it  gives  electricity  of  the  greatest 
intensity  ;  and,  in  the  second  way,  electricity  of  the  greatest 
quantity. 


292  ELECTRICITY. 

The  spark  obtained  from  a  powerful  Leyden  battery  can 
be  made  to  imitate  on  a  small  scale  all  the  effects  of  light- 
ning. It  can  be  made  to  split  tough  bits  of  wood,  shiver 
glass,  and  ihe  like. 

300.  The  Effect  of  Points  on  a  Conductor.  —  It  is  found  to 
be  impossible  to  charge  a  conductor  when  a  sharp  point 
projects  from  it,   or  is  held  near  it.     The  point  conveys 
away  the  electric  force  silently.     If   the  hand   is   held  in 
front  of  the  point  when  the  electricity  is  developed,  a  cur- 
rent of  air  is  distinctly  felt  setting  off  from  the  point.     If  a 
lighted  taper  is  held  near  the  point,  the  flame  is  blown 
away  from  it.     The  electric  force  is  then  evidently  carried 
off  by  the  molecules  of  the   air  which  form  the  current, 
and  hence  it  is  called    convective  discharge.      Since   in   a 
darkened  room  a  star  of  light  is  seen  upon  a  point  held 
near  a  powerful  electrical  machine  while  in  action,  this 
silent  discharge  is  also  called  glow  discharge. 

The  charge  rises  so  high  at  the  point  that  the  molecules 
of  air  just  about  it  are  strongly  polarized.  They  then 
seem  to  act  like  little  pith  balls.  The  molecules  directly 
in  front  of  the  point  are  first  attracted  and  then  repelled  ; 
while  those  just  behind  are  in  turn  drawn  to  the  point  and 
then  driven  from  it,  giving  rise  to  a  current  of  air  from  the 
point. 

301.  The  Electric  Wheel.  —  As  each  molecule  is  repelled 
from  the  point,  it  also  repels  the  point  itself,  which,  if  free 
to  move,  ought  to  move  as  well  as  the  molecules  of  air. 

Fig.  212.  This  explains  the  action  of  the  electric  ivheel, 
which  consists  of  a  number  of  points  all  bent 
round  in  the  same  direction,  as  shown  in  Figure 
212.  The  wheel  is  poised  so  as  to  turn  easily, 
and  when  connected  with  the  prime  conductor  of 
the  machine  in  action,  it  rotates  rapidly,  each 

point  moving  backwards. 


ELECTRICITY.  293 


SUMMARY. 

When  unlike  substances  are  rubbed  together,  frictional 
electricity  is  developed.  (288.) 

Frictional  electricity  has  slight  quantity  but  enormous 
tension  ;  while  voltaic  electricity  has  slight  tension  but 
enormous  quantity.  (289.) 

Two  opposite  electrical  forces  are  developed  on  the  two 
conductors  of  the  electrical  machine  ;  and  one  cannot  be 
developed  without  at  the  same  time  developing  the  other. 
(291,  292.) 

A  body  is  polarized  when  it  has  opposite  electrical  forces 
developed  on  opposite  parts  ;  it  is  charged  when  it  has  only 
one  electrical  force  upon  it. 

A  body  charged  with  either  electrical  force  polarizes  an 
insulated  conductor  near  it,  inducing  upon  the  face  nearest 
itself  the  opposite  electrical  force.  The  polarized  condi- 
tion of  such  a  conductor  depends  upon  the  non-conducting 
medium  between  the  two  bodies.  (293,  294.) 

The  charge  which  a  body  can  receive  depends  upon  the 
readiness  with  which  it  can  carry  on  polarization,  as  is 
shown  in  the  case  of  the  Leyden  jar.  (297,  298.) 

The  action  of  points  on  charged  bodies  is  to  convey  the 
charge  off  silently  by  convective  discharge.  (300.) 


ELECTRICAL   MACHINES  AND    APPLICATIONS 
OF  ELECTRICITY. 

MACHINES    FOR   DEVELOPING   ELECTRICITY. 

302.  Magneto-electric  Machines.  —  The  batteries  for  de- 
veloping voltaic  electricity  have  already  been  described. 

An  instrument  for  developing  electricity  by  means  of  mag- 
netism is  called  a  magneto-electric  machine.  In  ordinary  ma- 


294 


ELECTRICITY. 


Fig.  213. 


chines  of  this  kind  the  electricity  is  induced  by  means  of  a 
variable  magnet :  there  must,  therefore,  be  some  means  of 
developing  and  destroying  magnetism  in  a  piece  of  soft 
iron.  The  iron  is  placed  inside  a  helix,  which  serves  as  a 
conductor  for  the  current  induced.  The  magnetism  may 
be  developed  and  destroyed  by  means  either  of  a  perma- 
nent magnet  or  of  an  electric  current. 

The  former  method  is  illustrated  by  Figure  213.     JVS  is 
a  permanent  horseshoe  magnet      C  D  is  a  bar  of  soft  iron 

with  coils,  A  and  B,  wound 
round  its  ends,  and  may  be 
viewed  as  the  armature  of  the 
magnet.  C  D  is  capable  of 
rotation  round  the  axis  E  F. 
So  long  as  CD  remains  at  rest, 
no  currents  are  induced  in  the 
coils,  for  no  change  takes  place 
in  the  magnetism  induced  in 
it  by  the  action  of  N  S.  But 
if  the  poles  of  C  D  leave  N  S, 
the  magnetism  of  the  soft  iron 
diminishes  as  its  distance  from 
N  S  increases,  and  when  it 
stands  at  right  angles  to  its  former  position,  the  magnetism 
has  disappeared.  During  the  first  quarter-revolution,  there- 
fore, the  magnetism  of  the  soft  iron  diminishes,  and  an 
electric  current  is  induced  in  the  coils.  During  the  second 
quarter-revolution  the  magnetism  of  the  armature  increases 
till  it  reaches  a  maximum  when  its  poles  are  in  a  line  with 
those  of  IV  S.  A  current  also  marks  this  increase,  and 
moves  in  the  same  direction  as  before  ;  for  though  the 
magnetism,  increases  instead  of  diminishing,  which  of  itself 
would  reverse  the  induced  current,  the  poles  of  the  arma- 
ture, having  changed  their  position  with  relation  to  those 
of  the  permanent  magnet,  have  also  been  reversed,  and 


ELECTRICITY. 


295 


Fig.  214. 


this  double  reversal  leaves  the  current  to  move  as  before. 
For  the  second  halt-revolution  the  current  also  moves  in 
one  direction,  but  opposite  to 
that  of  the  first  half-revolution, 
since  the  position  of  the  arma- 
ture is  reversed.  Thus  in  one 
revolution  of  a  soft  iron  armature 
in  front  of  the  poles  of  a  perma- 
nent magnet,  two  currents  are  in- 
duced in  the  coils  encircling  //,  each 
lasting  half  'a  revolution,  starting 
from  the  line  joining  the  poles. 

The  manner  in  which  the 
armature  may  be  made  to  ro- 
tate, and  the  current  to  flow 
constantly  in  one  direction,  is 
shown  in  Figure  214,  which 
represents  a  common  form  of 
magneto-electric  machine.  NS 
is  a  fixed  permanent  magnet. 
B  B  is  a  soft  iron  plate,  to  which  are  attached  two  cylin- 
ders of  soft  iron,  round  which  the  coils  Cand  D  are  wound. 
C  B  B  D  is  thus  the  revolving  armature,  corresponding 
to  CD  in  Figure  213.  A  A  is  a  brass  rod  attached  to  the 
armature,  and  serving  as  its  axle.  ./MS  a  cylinder  fastened 
to  A,  and  is  pressed  upon  by  two  fork-like  springs,  Zf  and 
K,  which  are  also  the  poles  of  the  machine.  The  ends  m 
and  n  of  the  coil  are  soldered  to  two  metal  rings  on  F,  in- 
sulated from  each  other.  When  the  armature  revolves, 
A  A  and  F  move  with  it.  F,  H,  and  ^are  so  constructed 
as  to  reverse  the  current  at  each  half-revolution.  By  this 
arrangement,  the  opposite  currents  proceeding  from  the  coil 
at  each  half-revolution  are  so  transmitted  to  Zf  and  K>  that 
these  retain  their  polarity  unchanged.  When  the  armature 
is  made  to  revolve  rapidly,  a  very  energetic  and  steady 


296 


ELECTRICITY. 


current  is  generated,  which  has  all  the  properties  of  the  gal- 
vanic current.  Compared  with  the  galvanic  battery,  the 
magneto-electric  machine  is  a  readier,  steadier,  and  clean- 
lier §ource  of  electricity,  and  has  come  to  be  extensively 
used  instead  of  it.  Magneto-electric  machines  may  be 
made  of  any  strength  by  increasing  the  number  of  magnets 
and  the  mechanical  force  employed. 

In  large  machines,  several  magnetic  batteries  are  em- 
ployed. The  coils  may  be  arranged,  like  the  cells  of  a  gal- 
vanic battery,  for  tension  or  for  quantity.  For  giving 

shocks,  or  for  electrol- 
ysis, the  wire  used 
must  be  long  and  fine  ; 
for  heating  platinum 
wire,  thicker  and  short- 
er. The  electric  force 
increases  with  the  ra- 
pidity of  rotation. 


215. 


c 


303.  Wilde's  Mag- 
neto-electric Machine,  — 
A  magneto-electric  ma- 
chine of  great  power 
has  been  recently  in- 
vented by  Mr.  Wilde, 
of  Manchester,  Eng- 
land. A  front  view  of 
the  machine  is  shown 
in  Figure  215.  M  is 
the  foremost  of  a  se- 
ries of  sixteen  power- 
ful steel  magnets  of 
horseshoe  form,  placed 
one  behind  another  in  a 
horizontal  row.  These 
magnets  are  fixed  be- 


ELECTRICITY.  2Q7 

low  to  the  magnet  cylinder,  shown  on  a  larger  scale  in 
Figure  216.  This  is  made  partly  of  iron,  partly  of  brass. 
The  sides  /  /  are  of  iron,  and  the  brass  bars  b  b  lie  be- 
tween them.  In  the  centre  is  a  circular  hole  extending 
the  whole  way  through.  The  magnets  are  firmly  fastened 
to  the  iron  sides  /  /,  so  that  the  latter  form  the  poles  of 
the  magnetic  battery,  the  brass  bars  between  them  insulat- 
ing them  from  each  other. 

A  cylindrical  armature  a  a  of  cast  iron  is  made  to  re- 
volve within  the  magnet  cylinder.  Its  diameter  is  a  little 
less  than  that  of  the  cylindrical  hole,  so  that  it  can  revolve 
without  friction  very  close  Fig.  2l6. 

to  the  polar  surfaces.  It 
is  shown  in  section  in  Fig- 
ure 216.  Two  rectangu- 
lar grooves  are  cut  in  it, 
as  there  represented,  and 
in  these  about  fifty  feet  of 
insulated  copper  wire  is 
wound  lengthwise  in  three 
coils.  The  coil  thus  formed  is  shut  in  by  wooden  packing, 
c  c.  Two  caps  of  brass  are  fitted  to  the  ends  of  the  arma- 
ture, and  to  these  are  attached  the  steel  axes  of  rotation. 
The  rear  axis  is  connected  by  means  of  a  pulley  and  belt 
with  the  engine  which  rotates  the  armature.  On  the  front 
axis  are  two  metallic  pieces,  one  connected  with  the  arma- 
ture, and  the  other  insulated  from  it.  One  end  of  the 
armature  coil  is  connected  with  the  armature,  and  thus 
with  one  of  these  metallic  pieces,  and  the  other  end  is 
insulated  from  the  armature  and  connected  with  the  other 
piece  ;  so  that  these  metallic  pieces  are  the  terminals  of 
the  coil.  Two  steel  springs  press  against  these  pieces, 
each  spring  against  one  piece  during  half  a  rotation.  In 
the  position  shown  in  Figure  216,  the  armature  is  magnet- 
ized, since  the  parts  a  a  are  facing  the  poles  of  the  per- 
13* 


298  ELECTRICITY. 

manent  magnets.  On  performing  a  quarter-revolution,  the 
armature  loses  its  magnetism,  since  its  poles  are  carried 
away  from  the  poles  of  the  magnets.  After  another  quar- 
ter-revolution, it  again  becomes  magnetic,  and  so  on ;  so 
that  in  one  revolution  the  armature  induces  two  opposite 
currents  in  the  coil,  one  in  each  half-revolution.  The 
springs  act  in  such  a  way  that  the  current  passes  through 
them  always  in  the  same  direction.  The  armature  is  made 
to  revolve  some  2,500  times  per  minute,  sending  5,000 
waves  or  currents  of  electricity  to  the  wires  o  o. 

One  advantage  of  the  position  of  the  armature  in  this 
machine  is  that  its  motion  is  not  resisted  by  the  air.  In 
the  ordinary  magneto-electric  machines  (see  Figure  214) 
much  of  the  mechanical  force  applied  to  the  rotation  is 
wasted  in  beating  the  air. 

Another  advantage  is  that  the  inductive  action  of  the 
magnet  is  exerted  directly  on  the  coil,  as  well  as  through 
the  intervention  of  the  armature.  If  the  coil  were  made 
to  rotate  without  the  armature,  currents  would  be  induced 
in  it  of  the  same  kind  as  that  induced  by  the  armature, 
though  of  feebler  intensity  ;  and  these  currents  would  be 
strongest  when  the  coil  was  moving  through  the  line  join- 
ing the  poles,  and  weakest  when  it  was  at  right  angles  to 
that  position.  The  currents  induced  by  the  armature  are 
strongest  when  those  just  mentioned  are  weakest,  and 
weakest  when  those  are  strongest ;  so  that  armature  and 
coil  combine  to  make  the  current  uniform. 

But  the  chief  peculiarity  and  merit  of  Wilde's  machine 
is  that  the  current  got  from  the  magneto-electric  apparatus 
is  not  directly  made  use  of,  but  is  employed  to  magnetize 
an  electro-magnet,  E  E  (Figure  215),  some  hundreds  of 
times  more  powerful  than  the  magnetic  battery  originally 
employed,  and  this  electro-magnet  is  made  to  induce  an- 
other and  proportionally  more  powerful  current  by  means 
of  a  second  rotating  armature.  The  upper  and  lower 


ELECTRICITY.  299 

machine  are  in  action  precisely  alike ;  only  the  upper 
magnet  is  a  permanent  magnet,  and  the  lower  one  an 
electro-magnet.  We  have  the  same  magnet  cylinder,  the 
same  armature,  springs,  and  poles.  This  armature  is  made 
to  rotate  some  1,800  times  per  minute. 

A  machine  intended  for  a  three-horse  power  steam- 
engine,  and  worked  with  that  power,  will  consume  carbon 
sticks  three  eighths  of  an  inch  square,  and  evolve  a  light 
of  surpassing  brilliancy.  With  a  machine  consuming  car- 
bons half  an  inch  square,  the  light  is  of  sufficient  intensity 
to  cast  shadows  from  the  flames  of  street-lamps  a  quarter 
of  a  mile  off.  The  same  light,  at  two  feet  from  the  re- 
flector, darkened  photographic  paper  as  much  in  twenty 
seconds  as  the  direct  rays  of  the  sun  at  noon  in  one 
minute. 

Wilde's  machine  enables  us  to  convert  any  amount  of 
mechanical  force  into  electricity  by  increasing  the  size  of 
the  electro-magnet,  or  by  using  a  second  electro-magnet 
induced  by  the  first ;  so  that  a  magnet  indefinitely  weak  can 
be  made  to  induce  a  current  or  a  magnet  of  indefinite  strength. 
The  size  and  weight  of  the  apparatus  are  also  small. 

304.  Induction  Coils.  —  When  the  magnetism  is  devel- 
oped and  destroyed  by  means  of  a  current,  the  soft  iron 
must  be  placed  inside 
a  coil  through  which 
the  current  is  sent. 
This  is  called  the/;7- 
mary  coil,  and  must 
be  placed  inside  an- 
other coil,  called  the 
secondary  coil,  which 
serves  as  a  conductor 
of  the  induced  elec- 
tricity. Such  a  machine 
is  commonly  called  an 


300  ELECTRICITY. 

induction  coil.  In  the  one  shown  in  Figure  217,  the 
primary  coil  is  of  coarse  wire  wound  with  wool,  and  is 
attached  to  the  wooden  base  of  the  instrument.  The 
secondary  coil  is  of  finer  silk-wound  wire,  much  longer 
than  the  primary  wire.  Within  the  primary  coil  is  a 
bundle  of  iron  wires,  which  are  sufficiently  insulated  by 
the  rust  that  gathers  on  them.  The  developing  of  mag- 
netism in  these  wires  is  the  chief  aim  of  the  primary  coil, 
and,  as  a  strong  current  is  necessary  for  that  purpose, 
coarse  wire  is  used  in  that  coil.  In  the  secondary  coil,  the 
tension  of  the  induced  current  alone  is  aimed  at,  and  fine 
wire  is  used,  so  that  as  many  turns  as  possible  may  be 
brought  within  the  influence  of  the  primary  coil  and  its 
core ;  for  it  is  found  that  the  tension  of  the  induced  cur- 
rent is  proportional  to  the  strength  of  the  primary  cur- 
rent, and  to  the  square  of  the  resistance  in  the  secondary 
coil. 

In  order,  however,  to  obtain  the  greatest  effect  from  the 
secondary  coil,  it  is  necessary  to  have  some  means  of  rap- 
idly completing  and  breaking  the  primary  current.  This 
is  effected  in  the  instrument  under  consideration,  either  by 
means  of  the  rasp  seen  behind  the  coils,  or  by  the  self- 
acting  rheotome  (that  is, 'current-cutter]  at  the  left  hand. 
When  the  former  is  used,  one  of  the  battery  wires  is  at- 
tached to  one  of  the  binding-screws,  and  thereby  to  one 
end  of  the  primary  coil ;  and  the  other  battery  wire  is 
drawn  along  the  teeth  of  the  rasp,  which  is  connected  with 
the  other  end  of  the  coil.  The  current  is  stopped  and 
started  again  every  time  the  wire  passes  from  one  tooth  to 
another ;  and  every  time  it  is  stopped  or  started,  an  inverse 
or  a  direct  current  is  excited  in  the  secondary  wire.  The 
rheotome  breaks  the  current  in  the  same  way,  but  more 
regularly  and  rapidly.  When  it  is  used,  both  battery  wires 
are  attached  to  the  binding-screws,  bringing  the  rheotome 
and  the  primary  coil  into  the  circuit. 


ELECTRICITY. 


3OI 


305.  The  Inductorium,  or  Ruhmkorff  's  Induction  Coil. — 
The  essential  parts  of  this  apparatus,  like  those  of  the  one 
described   in  the  last  section,  are  a  primary  coil,  with  its 
core  of  iron  wire,  and  a  secondary  coil  outside  the  primary 
and  insulated  from  it.     The  primary  coil  is  connected  with 
a  galvanic  battery,  and  a  rheotome  is  used   to  interrupt 
the  current,  as  already  explained. 

A  RuhmkorrT's  coil  of  moderate  size  readily  yields 
sparks  of  from  four  to  five  inches,  with  a  battery  of  six 
Bunsen's  cells.  The  power  of  the  induced  current  to  de- 
flect the  needle  of  the  galvanometer,  and  to  effect  electrol- 
ysis, is  very  insignificant.  This  shows  that  it  is  very  much 
inferior  to  the  inducing  current  in  quantity,  however  much 
it  may  be  superior  in  tension.  The  physiological  effect, 
however,  is  tremendous,  and  the  experimenter  must  take 
care  not  to  allow  any  part  of  his  body  to  form  the  medium 
of  communication  between  the  poles,  as  the  shock  might 
be  dangerous,  if  not  fatal. 

306.  Foucaulfs  Self-acting  Rheotome.  —  The  best  rheo- 
tome for   use  with   the  inductorium   is   Foucault's.     This 
instrument  is  shown  in  Figure  218,  and  illustrates  one  of 

Fig.  218. 


3O2  ELECTRICITY. 

the  many  applications  of  the  electric  force  to  doing  me- 
chanical work.  It  consists  of  a  beam,  a  d,  supported  by  a 
standard  C  G,  which  acts  as  a  spring.  At  one  end  of  the 
beam  there  is  a  keeper  of  soft  iron;  at  the  other  end,  two 
iron  rods,  which  plunge  into  cups  A,  B,  partially  filled  with 
mercury.  Under  the  iron  keeper  is  an  electro-magnet,  D. 
One  end  of  the  wire  of  the  helix  of  this  magnet  connects 
with  one  pole  of  a  Bunsen's  cell.  The  other  pole  of  this 
cell  is  connected  with  the  mercury  cup,  B.  The  other  end 
of  the  wire  of  the  helix  is  connected  with  the  beam  by 
means  of  the  standard  ;  so  that  the  circuit  of  the  Bunsen's 
cell  is  closed  when  the  iron  rod  dips  into  the  mercury, 
and  is  open  when  it  is  out  of  the  mercury.  It  is  best 
to  cover  the  mercury  with  alcohol,  which  is  a  non-con- 
ductor. 

When  the  rheotome  is  to  be  worked,  the  iron  rod  is  so 
adjusted  that  its  end  is  just  above  the  surface  of  the  mer- 
cury. That  end  of  the  beam  is  then  depressed  by  the 
hand  so  as  to  bring  the  rod  into  the  mercury.  This  closes 
the  circuit,  and  renders  the  electro-magnet  active,  and  the 
keeper  at  the  end  of  the  beam  is  drawn  down  upon  it. 
This  carries  the  other  end  of  the  beam  up  and  the  rod  out 
of  the  mercury,  opens  the  circuit,  and  renders  the  electro- 
magnet inactive.  The  elasticity  of  the  standard  throws 
this  end  of  the  beam  back  and  lowers  the  rod  into  the 
mercury,  closing  the  circuit  again,  and  the  same  succession 
of  movements  is  repeated  indefinitely. 

This  instrument  is  made  to  open  and  close  a  second 
circuit  in  the  following  manner.  One  pole  of  the  battery 
of  this  circuit  is  connected  with  the  beam,  and  so  with  the 
iron  rod,  which  dips  into  the  second  cup  of  mercury,  A, 
which  is  connected  with  the  other  pole  of  the  battery  ; 
so  that  this  circuit  is  closed  when  the  rod  dips  into  the 
mercury,  and  open  when  it  is  out  of  the  mercury.  But  if 
the  point  of  the  rod  is  so  adjusted  as  to  be  just  above  the 


ELECTRICITY.  303 

surface  of  the  mercury,  it  is  drawn  out  of  it  every  time 
that  the  keeper  is  drawn  down  to  the  electro-magnet,  and 
is  plunged  into  it  every  time  that  the  keeper  is  thrown 
back  by  the  spring. 

307.  Geissler's  Tubes.  —  A  variety  of  forms  of  apparatus 
are  used  for  showing  the  electric  light  in  rarefied  air  and 
in  other  gases.*  Geissler's  tubes,  so  called  from  the  in- 
ventor, are  combinations  of  bulbs  and  tubes,  filled  with 
rarefied  gases  and  liquids,  and  then  sealed  air-tight,  so  as 
to  be  ready  for  use  at  any  time.  One  of  them  is  shown  in 


Figure  219.  When  the  current  is  sent  through  these  tubes, 
they  exhibit  lights  of  various  tints  according  to  the  gases 
contained  in  them. 


SUMMARY. 

IN  ordinary  magneto-electrical  machines  electricity  is 
induced  by  developing  and  destroying  magnetism  in  soft 
iron  placed  inside  a  helix.  This  may  be  done  by  using  a 
permanent  magnet,  or,  as  in  the  various  forms  of  induction 
coils,  by  means  of  the  current.  (302,  304,  305.) 

In  Wilde's  machine,  the  electricity  obtained  by  means  of 
permanent  magnets  is  made  to  develop  much  more  power- 
ful magnetism  in  a  large  electro-magnet,  which  in  turn  is 
made  to  develop  electricity.  In  this  way  a  magnet  in- 
definitely weak  may  be  made  to  develop  a  current  in- 
definitely strong.  (303.) 

*  All  the  experiments  with  the  electric  light  usually  performed  by 
means  of  Frictional  Electricity  can  be  better  performed  with  the  /«- 
ductoriitm.  See  Appendix,  Note  8. 


3  c>4  ELECTRICITY. 


APPLICATIONS   OF   ELECTRICITY. 

308.  Electrotyping. — When  the  solution  of  cupric  sul- 
phate is  decomposed  slowly,  the  copper  is  deposited  on  the 
cathode  in  a  coherent  mass,  which  may  be  stripped  off 
when  it  has  become  sufficiently  thick.  The  sheet  of  copper 
stripped  off  is  found  to  present  a  perfect  reverse  image  of 
the  face  of  the  cathode,  the  faintest  lines  being  copied  with 
perfect  distinctness.  If  this  reverse  image  be  now  made 
the  cathode,  and  another  sheet  of  copper  be  deposited 
upon  it,  an  exact  copy  of  the  original  electrode  is  obtained. 
Any  conducting  substance,  of  whatever  size  and  shape, 
may  be  made  a  cathode  by  simply  connecting  it  with  the 
negative  pole  of  the  battery.  Hence  coins,  medals,  and 
engraved  plates  may  be  copied  with  perfect  accuracy,  and 
with  but  slight  trouble  and  expense. 

This  process  of  copying  by  means  of  electricity  is  called 
electrotyping. 

The  face  of  a  medal  may  be  copied  by  making  it  the 
cathode  and  depositing  a  sheet  of  copper  upon  it,  and  then 
depositing  another  sheet  of  copper  upon  this  sheet  after  it 
has  been  separated  from  the  medal.  In  practice,  however, 
a  mould  of  the  thing  to  be  copied  is  first  taken  in  some  soft 
substance,  such  as  plaster,  gutta-percha,  or  wax,  and  this 
mould  is  made  the  cathode.  If  the  mould  is  made  of  non- 
conducting material,  as  is  usually  the  case,  its  surface  must 
be  covered  with  some  conducting  substance,  as  powdered 
graphite.  The  mould  may  be  covered  by  means  of  a  hair 
brush  with  a  film  of  graphite  sufficient  to  make  it  a  con- 
ductor, without  obliterating  the  finest  lines. 

One  of  the  chief  uses  of  electrotyping  is  in  copying 
printer's  type  after  it  has  been  set  up,  and  in  copying  wood 
engravings.  An  impression  is  taken  of  the  type  or  of  the 
engraving  in  wax.  This  wax  is  then  brushed  over  with 


ELECTRICITY. 


3^5 


powdered  graphite,  and  made  the  cathode  ;  the  electrolyte 
is  cupric  sulphate,  and  the  anode  a  piece  of  copper. 

A  large  bath  is  used  (see  Figure  220),  so  that  several 

Fig.  220. 


pieces  may  be  electrotyped  at  the  same  time.  These  are  all 
hung  by  wires  to  a  metallic  rod  which  is  connected  with 
the  negative  pole  of  the  battery.  Upon  another  metallic 
rod  pieces  of  copper  are  hung  opposite  to  the  pieces  to  be 
copied. 

The  electric  current  is  sometimes  generated  in  the  bath 
itself.  The  object  to  be  coated  serves  as  one  of  the  plates 
of  the  battery,  and  a  piece  of  zinc  as  the  other,  the  wire 
connecting  the  two  being  coated  with  insulating  varnish. 

309.  Electro-plating.  — This  is  the  art  of  coating  the 
baser  metals  with  silver  by  the  electric  current.  Articles 
to  be  electro-plated  are  generally  made  of  brass,  bronze, 
copper,  or  nickel  silver,  this  last  being  the  best  material. 

The  bath  is  a  large  trough  of  earthen-ware  or  other  non- 
conducting substance.  It  contains  a  weak  solution  of 
argentic  cyanide  (cyanide  of  silver)  and  potassic  cyanide 
(cyanide  of  potassium).  A  plate  of  silver  forms  the  anode ; 
and  the  articles  to  be  plated,  hung  by  wires  to  a  metal 
rod  lying  across  the  trough,  constitute  the  cathode.  When 
the  former  is  connected  with  the  positive  pole  of  a  bat- 
tery, and  the  latter  with  the  negative  pole,  the  silver  of 

T 


306 


ELECTRICITY. 


the  cyanide  begins  to  deposit  itself  on  the  suspended 
articles,  and  the  cyanogen,  set  free  at  the  plate,  dissolves 
it,  forming  argentic  cyanide.  The  thickness  of  the  plat- 
ing depends  on  the  length  of  time  the  articles  are  im- 
mersed. 

310.  Electro-gilding. — This  process  is   essentially  the 
same  as  electro-plating,  except  that  the  articles  are  coated 
with  gold  instead  of  silver.     The  electrolyte  in  this  case  is 
the  cyanide  or  some  other  salt  of  gold,  and  the  anode  is  a 
lump  of  gold.     If  it  is  not  intended  to  gild  the  whole  sur- 
face of  the  article,  the  parts  not  to  be  gilded  must  be  coated 
with  some  non-conducting  substance. 

311.  Electro-metallurgy.  —  Many  other  metals  besides 
copper,  silver  and  gold  may  be  deposited  by  electrolysis. 
The  art  of  depositing,  by  electro-chemical  action,  a  metal 
on  any  surface  prepared    to  receive   it,  is   called   electro- 
metallurgy.    All  processes  of  the  kind  may  be  classified  in 
two  divisions,  one  of  which  is  illustrated  by  electrotyping, 
and  the  other  by  electro-plating.     The  former  includes  all 
those   cases  in  which  the  coating  of  metal  is  to  be  re- 
moved from  the  surface  on  which  it  is  deposited  ;  and  the 
latter  all  cases  where   the  coating   remains  permanently 
fixed.     Gold,  platinum,  silver,  copper,  zinc,  tin,  lead,  cobalt, 
and  nickel  can  be  deposited  by  electrolysis. 

312.  Electric  Clocks.  —  The  elec- 
tric force  has  also  been  used  to  reg- 
ulate the  movements  of  clocks,  called 
copying  clocks.  They  are  of  the  usual 
construction,  except  that  the  pendu- 
lum balls  are  hollow  coils  of  copper 
wire,  so  that  they  become  magnetic 
when  a  current  is  sent  through  them. 
In  Figure  221,  £  represents  a  part 
of  the  rod,  and  B  the  ball,  of  such 
a  pendulum.  Permanent  magnets, 


ELECTRICITY. 


307 


N S  and  S  JV,  are  fastened  against  the  sides  of  the  clock- 
case  opposite  the  ends  of  the  coil  B,  with  like  poles  to- 
wards the  coil.  The  hollow  of  the  coil,  as  it  swings,  can 
pass  a  little  way  up  the  length  of  each  magnet.  If  the 
south  poles  of  the  magnets  are  turned  towards  the  coil, 
as  in  the  figure,  and  a  current  is  sent  through  the  wire,  one 
end  of  the  coil  becomes  a  north  pole,  which  is  attracted 
by  the  magnet  near  it,  and  the  other  end  a  south  pole, 
which  is  repelled  by  the  magnet  near  it.  This  attraction 
and  repulsion  both  tend  to  send  the  coil  in  one  direction. 
If,  now,  at  the  instant  that  B  is  drawn  to  one  side,  the  di- 
rection of  the  current  is  changed,  the  poles  of  the  coil  are 
reversed,  and  it  is  carried  to  the  other  side.  The  pendu- 
lum thus  vibrates  every  time  the  current  is  reversed.  This 
is  done  by  means  of  a  standard  or  regulating  clock.  Every 
time  the  pendulum  of  this  clock  vibrates,  the  direction  of 
the  current  is  reversed ;  so  that  the  pendulums  of  all  the 
copying  clocks  vibrate  exactly  at  the  same  rate  as  the  pen- 
dulum of  the  regulating  clock.  In  this  way,  by  means  of 
one  accurate  clock,  any  number  of  copying  clocks,  of  the 
most  ordinary  construction,  can  be  made  to  keep  accurate 
time. 

Fig.    222. 


..I... 


Figure  222  shows  one  of  the  ways  in  which  the  pendulum, 
A,  of  the  regulating  clock  can  change  the  direction  of  the 
current.  The  spring  e  is  connected  with  the  negative  pole 


308  ELECTRICITY. 

of  the  battery  G,  and  the  spring  d  with  the  positive  pole  of 
the  battery  F.  The  other  poles  of  these  batteries  are  con- 
nected with  the  plates  m  and  ;z,  buried  in  the  earth.  B 
and  C  are  the  pendulums  of  the  copying  clocks.  When 
the  regulating  pendulum  touches  the  spring  d,  the  current 
flows  through  the  wire  from  A  to  B  and  C ;  when  uv  touches 
the  spring  e,  the  current  flows  first  through  the  eartH  from 
11  to  o,  and  then  through  the  wire  from  C  to  A.  The  Der- 
manent  magnets  connected  with  the  pendulums  B  and  <C 
are  not  represented  in  the  diagram. 

313.  The  Electric  Telegraph.  —  Since  the  electric  current 
passes  with    comparatively  little  resistance   through  thick 
conductors  of  almost  any  length,  it  is  now  much  used  in 
transmitting  signals  between  distant  stations.     An  instru- 
ment for  sending  such  signals  is  called  a  telegraph.     The 
word  literally  means  writing  at  a  distance. 

Four  things  are  essential  in  every  kind  of  electric  tele- 
graph :  (i.)  a  battery  for  generating  the  electricity;  (2.) 
wires  for  conducting  the  electricity ;  (3.)  an  instrument  for 
sending  the  message  ;  and  (4.)  an  instrument  for  receiving 
the  message. 

The  battery  used  is,  in  almost  all  cases,  a  voltaic  battery. 
The  sending  instrument  is  merely  a  key  for  opening  and 
closing  the  circuit,  or  for  changing  the  direction  of  the  cur- 
rent. The  receiving  instrument,  in  the  needle  telegraph,  is 
a  magnetic  needle,  which  by  its  movements  indicates  the 
message  sent.  In  Bain's  chemical  telegraph,  an  iron  point 
makes,  while  the  current  is  passing,  blue  marks  upon  paper 
by  decomposing  the  prussiate  of  potash  with  which  the 
paper  has  been  saturated.  Many  other  forms  of  telegraph 
have  been  invented,  but  the  two  most  used  at  the  present 
time  are  Morses  and  the  Combination  Printing  Telegraph. 

314.  Morse's  Telegraph.  — This  telegraph  depends  on  the 
power  of  the  current  to  develop  magnetism  in  soft  iron, 
and  hence  is  an   electro-magnetic  telegraph. 


ELECTRICITY. 


309 


The  essential  parts  of  the  receiving  instrument  are  shown 
in  Figure  223.     One  of  the  screw-cups  at  the  right  is  — 


con- 


Fig.  223. 


nected  with  the  line  wire  from  the  distant  station,  and  the 
other  with  the  earth.  The  current  traverses  the  coils  of 
the  electro-magnet,  and  draws  down  the  keeper  and  the 
arm  of  the  lever  to  which  it  is  attached.  The  other  end 
of  the  lever  is  raised,  pressing  a  steel  point,  or  style,  against 
a  strip  of  paper,  which  is  unrolled  from  the  bobbin  above, 
and  moved  steadily  along  by  clock-work  not  represented  in 
the  figure.  When  the  current  from  the  distant  station  is 
broken,  the  shorter  arm  of  the  lever  is  released  by  the 
electro-magnet,  the  longer  arm  falls  back  by  its  weight, 
and  the  style  ceases  to  press  against  the  paper.  The  kind 
of  mark  made  upon  the  paper  depends  upon  the  time  the 
style  remains  elevated.  If  it  is  raised  for  a  moment  only, 
a  dot  is  made  ;  if  for  a  longer  time,  a  dash.  The  alphabet 
used  is  made  up  by  the  combination  of  dots  and  dashes. 
The  following  is  the  usual  Morse  alphabet :  — 


310 


ELECTRICITY. 


A 
B 

C 

D 

E- 

F. 

G 

H 

I  - 


j 

K 

L- 

M 

N— - 
O-  - 

P 

Q 

R-   -- 


S- 
T 
U 
V- 

w 

X 
Y 
Z- 

& 


The  letters  occurring  most  frequently  are  most  easily 
signalled  ;  thus,  E  is  one  dot ;  T,  one  dash.  An  expert 
operator  can  transmit  from  thirty  to  forty  words  a  minute 
on  a  land  line  of  from  200  to  300  miles. 

A  clerk  accustomed  to  a  Morse  telegraph  seldom  looks 
at  the  paper  in  transcribing.  The  mere  clicking  of  the  lever 
becomes  a  language  perfectly  intelligible  to  him. 

315.   The  Sending  Instrument.  —  The  sending  instrument, 

or  transmitting  key,  is 
shown  in  Figure  224. 
A  brass  lever,  /  /,  moves 
on  the  axis  A.  It  has 
two  projections  of  plati- 
num, m  and  «,  on  its 
lower  side.  These  strike 


A 


against  pieces  of  platinum  b  and  a,  the  first  of  which  is  con- 
nected with  the  earth-wire  E ;  the  second,  by  the  wire  c,  with 
one  of  the  poles  of  the  sending  battery.  When  the  lever 
is  left  to  itself,  n  and  b  are  in  contact  under  the  force  of 
the  spring  S.  When  the  hand  presses  on  the  ebony  handle 
Jf,  contact  is  broken  at  n  and  b,  and  established  at  m  and 
a.  Besides  the  wires  E  and  c  already  mentioned,  the  line 
wire  Z,  from  the  distant  station,  is  connected  with  the 
lever,  through  its  axis,  A.  When  the  key  is  in  the  receiv- 
ing position  (as  shown  in  the  figure),  the  current  from  the 


ELECTRICITY.  311 

sending  station  takes  the  route,  Z,  A,  /,  «,  l>,  £,  the  record- 
ing instrument,  then  to  earth.  When  7/is  pressed  down, 
the  key  is  in  the  sending  position,  and  transmits  the  bat- 
tery current  by  c,  a,  m,  A,  Z,  to  the  distant  station. 

316.  The  Earth.  — One  wire  is  quite  sufficient  to  con- 
nect two  telegraph  stations,  if  its  terminations  be  formed  by 
two  large  plates  sunk  in  the  earth.     The  plates  are  gener- 
ally of  copper,  and  should  have  a  surface  of  not  less  than 
twenty  square  feet ;  and  they  must  be  buried  so  deep  that 
the  earth  about  them  never  gets  dry.     The  gas  and  water 
pipes  in  a  town  make  an  excellent  earth,  or  earth-connec- 
tion.    When  the  earths  are  good,  the  current  passes  through 
the  earth  between  the  two  stations,  no  matter  what  may  be 
the  nature  of  the  region  it  has  to  pass,  —  plain  or  mountain, 
sea  or  land.     The  resistance  of  the  earth  to  the  current, 
compared  with  that  of  a  long  line,  is  next  to  nothing.     The 
earth  serves  the  purpose,  not  only  of  a  second  wire,  but  of 
one  so  thick  that  its  resistance  may  be  left  out  of  account. 
In   conducting    power,  for    equal    dimensions,  the    earth 
stands  much  inferior  to  the  wire  ;  but  then  its   thickness, 
so  to  speak,  is  indefinitely  greater,  and  hence  its  conduct- 
ing power,  on  the  whole,  is  superior. 

317.  The  Relay.  —  It  is  only  on  short  circuits,  generally 
of  less  than  fifty  miles,  that  the  receiving  instrument    is 
worked    directly  by  the  line  current.      On  long  circuits, 
direct  working  could  only  be  accomplished  by  an   enor- 
mous sending  battery.     The  loss  by  leakage  on  the  way  is 
very  considerable,  so  that  a  current  strong  at  starting  be- 
comes very  weak  before  it  reaches  the  station  to  which  it  is 
sent.     Besides,  the  leakage  is  the  greater,  the  greater  the 
number  of  cells  employed,  or  the  greater  the  tension  of  the 
battery.     It  is  found  a  much  better  arrangement  to  work 
the  receiving  instrument  by  a  local  current,  and  to  include 
in  the  line  circuit  a  very  delicate  instrument,  which  has 
only  to  make  or  break  the  local  circuit.     Such  an  instru- 


312  ELECTRICITY. 

ment  is  called  a  relay ^  and  is  shown  in  Figure  225.     The 
electro-magnet,  £,  of  the  relay  is  included  in  the  line  cir- 
cuit, instead  of  the  electro-magnet  of  the  receiving  instru^ 
Fig.  22S.  ment.    The  coil  is  long, 

and  of  very  fine  wire  ; 
and  a  very  faint  current 
is  sufficient  to  develop 
magnetism  in  the  core. 
The  keeper,  A,  of  the 
relay  is  attached  to  a 
lever,  <?**,  turning  on  the 
axis  a.  When  a  current 
is  sent  through  the  coil, 
the  lever  is  drawn  down,  and  the  end  e1  rests  on  the  screw 
S.  When  there  is  no  current,  the  elasticity  of  the  spring  s 
brings  it  back  against  the  screw  S1.  The  pillars  N  and  P 
are  connected  with  the  poles  of  the  local  battery.  The 
metal  spring  s  places  the  lever  e  e'  in  connection  with  P. 
The  screw  S  and  the  end  e1  of  the  lever,  then,  are  virtually 
the  poles  of  the  battery.  When  these  are  in  contact,  the 
local  current  flows,  and  it  stops  when  e'  is  brought  back 
against  the  insulated  screw  S'.  The  receiving  instrument 
is  included  in  the  local  circuit.  When  a  current  comes 
from  the  sending  station,  the  keeper  A  is  attracted,  e1  falls 
on  S,  the  local  circuit  is  closed,  and  the  receiving  instru- 
ment begins  to  print.  When  the  current  ceases,  e1  returns 
to  S',  and  the  style  of  the  receiving  instrument  is  with- 
drawn from  the  paper.  The  effect  is  thus  the  same  as  if 
the  line  current  printed,  and  not  the  local  current.  By  this 
means,  a  current  too  weak  to  work  the  receiving  instrument 
can  complete  the  local  circuit  and  print  legibly. 

318.  The  Combination  Printing  Telegraph. — The  Morse 
recording  instrument,  as  we  have  seen,  writes  by  means  of 
dots  and  dashes.  An  instrument  has  been  invented  by 
Mr.  Royal  E.  House,  a  native  of  Vermont,  which  records 


ELECTRICITY.  313 

the  message  in  plain  Roman  letters.  This  telegraph  is 
known  as  House's  Printing  Telegraph,  and  was  patented 
in  1848.  It  has  been  found  to  work  well,  and  has  been 
used  on  many  lines. 

In  1855,  Mr.  David  E.  Hughes  of  Kentucky,  after  ten 
years  of  persevering  labor,  produced  a  printing  telegraph 
on  a  new  principle,  simpler  in  construction  and  capable  of 
working  upon  long  circuits.  In  this  telegraph  each  electric 
impulse  sent  over  the  wire  prints  a  letter,  while  the  House 
instrument  requires  on  an  average  seven  impulses  for  each 
letter,  and  the  Morse  an  average  of  three  and  a  half  im- 
pulses. 

Both  these  printing  telegraphs  have  now  been  in  great 
measure  superseded  by  the  Combination  Telegraph  devised 
by  Mr.  Phelps  of  Troy,  N.Y.  This  instrument,  as  its  name 
indicates,  is  a  combination  of  the  principles  of  the  two  pre- 
ceding telegraphs,  with  certain  improvements,  originated 
by  Mr.  Phelps. 

The  sending  instrument  somewhat  resembles  a  piano  in 
outward  appearance.  On  the  key-board  are  twenty-eight 
keys,  upon  which  are  printed  the  twenty-six  letters  of  the 
alphabet,  a  dot,  and  a  dash.  Near  the  key-board  is  a  brass 
cylinder.  On  each  key  there  is  a  peg,  and  in  the  cylinder 
there  are  twenty-eight  cavities,  one  for  the  peg  of  each  key, 
so  arranged  that  each  peg  can  enter  its  own  cavity,  and  no 
other.  The  cavities  are  arranged  spirally  around  the  cylin- 
der, so  that  each  cavity  is  ^  of  the  circumference  of  the 
cylinder  behind  the  preceding  one.  The  cavity  is  so  formed 
that  the  peg  of  the  key,  on  entering  it,  is  carried  a  little  to 
the  left,  and  thus  completes  the  circuit  If  all  the  keys 
were  depressed  at  once,  the  circuit  would  be  closed  twen- 
ty-eight times  at  equal  intervals  during  one  rotation  of 
the  cylinder.  If  a  key  at  the  beginning  of  the  alphabet, 
and  another  at  the  middle,  were  depressed  and  kept  de- 
pressed during  one  rotation,  the  circuit  would  be  closed 


314  ELECTRICITY. 

twice,  and  the  interval  between  the  closings  would  be 
that  of  half  a  rotation.  By  means  of  this  instrument 
the  circuit  can  be  closed  with  great  precision  at  fixed 
intervals. 

At  the  receiving  station  there  is  a  small  disc,  called  the 
type-wheel,  on  the  edge  of  which  are  types  of  the  twenty-six 
letters  and  the  dot  and  dash,  arranged  at  equal  intervals. 
By  the  side  of  the  type-wheel  is  a  little  press  just  large 
enough  to  take  off  one  letter  from  the  type  wheel.  This 
press  is  forced  against  the  type-wheel  by  machinery.  When 
this  machinery  is  at  rest,  the  press  is  thrown  back  from  the 
type-wheel  by  a  spring.  A  strip  of  paper  is  carried  along 
between  the  type-wheel  and  the  press  at  such  a  rate  that  it 
advances  the  width  of  a  letter  every  time  the  press  is 
pushed  against  the  wheel. 

The  type-wheel  and  press  are  moved  by  clock-work,  as 
is  also  the  printing  cylinder  at  the  sending  station.  The 
clock-work  at  each  station  is  regulated  by  the  vibrations  of 
springs  which  are  capable  of  vibrating  the  same  number  of 
times  a  minute ;  so  that  the  printing  cylinder  and  the  type- 
wheel  move  at  exactly  the  same  rate.  The  two  instruments 
are  so  set  that  the  letter  A  on  the  type-wheel  is  opposite 
the  press  at  the  same  instant  that  the  cavity  in  the  printing- 
cylinder  corresponding  to  that  letter  is  under  the  peg  of  its 
key.  If  the  key  were  depressed  at  this  instant,  the  circuit 
would  be  closed,  an  electric  impulse  would  be  transmitted, 
and,  in  passing  through  the  coil  of  the  electro-magnet  at 
the  receiving  station,  would  render  it  active  and  cause  it  to 
draw  down  its  keeper.  To  this  keeper  is  attached  a  detent^ 
or  catch,  which  arrests  the  motion  of  the  machinery  that 
works  the  press.  When  the  keeper  is  drawn  down  by  the 
magnet,  this  detent  is  withdrawn,  the  press  is  driven  for- 
ward, and  the  letter  opposite  is  printed  on  the  paper. 
When  the  circuit  is  again  opened,  the  keeper  is  thrown 
back  by  means  of  a  spring,  the  detent  replaced,  and  the 


ELECTRICITY.  315 

press  removed  from  the  type-wheel  by  the  spring  arranged 
for  that  purpose.  Since  both  the  type-wheel  and  the  cylin- 
der rotate  at  the  same  rate,  it  is  evident  that,  when  the  peg 
of  any  key  enters  its  cavity,  the  letter  of  that  key  will  be 
printed  at  the  receiving  station.  Every  time  the  circuit  is 
closed,  —  that  is,  every  time  a  key  is  depressed,  —  the  de- 
tent is  withdrawn  from  the  wheel  that  moves  the  press,  and 
a  letter  is  printed  on  the  paper.  The  type-wheel  rotates  at 
the  rate  of  about  one  hundred  and  twenty  times  a  minute. 
The  ordinary  speed  of  this  instrument  is  two  thousand 
words  an  hour,  which  is  about  twice  as  fast  as  the  Morse 
can  work. 

319.  The  Telegraphic  Fire- Alarm. — The  electric  tele- 
graph is  now  extensively  used  for  indicating  the  locality 
of  fires  in  cities.  In  various  parts  of  the  city  are  small 
iron  boxes  called  signal-boxes.  They  are  all  numbered, 
and  connected  with  a  central  station  by  means  of  wires. 
By  turning  a  crank  which  is  found  inside  the  signal-box, 
the  circuit  is  opened  and  closed  in  such  a  way  as  to  tele- 
graph to  the  central  station  the  number  of  the  box.  When, 
therefore,  a  fire  occurs  in  the  neighborhood  of  any  box,  the 
box  is  opened,  the  crank  turned,  and  the  number  of  the 
box  telegraphed  to  the  central  station.  This  station  is  also 
connected  by  wire  circuits  with  several  bells  in  different 
parts  of  the  city,  and  the  operator,  by  means  of  the  elec- 
tric force,  rings  on  these  bells  the  number  of  the  box  near 
which  the  fire  is,  so  that  the  firemen  know  at  once  almost 
the  exact  locality  to  which  they  must  go. 

The  hammers  which  strike  the  bells  are  worked  by 
weights,  the  machinery  being  similar  ro  that  of  the  striking 
apparatus  in  an  ordinary  turret-clock.  The  train  of  wheels 
is  kept  from  moving  by  a  detent,  or  catch.  When  the 
current  passes,  it  develops  magnetism  in  an  electro-magnet, 
which  attracts  a  keeper  in  front  of  it.  This  keeper  sup- 
ports a  small  lever  poised  nearly  vertically,  and  weighted 


316  ELECTRICITY. 

with  a  little  ball  near  its  upper  end.  This  lever  is  tripped 
by  the  withdrawal  of  the  keeper,  and  in  falling  acquires 
sufficient  force  to  strike  up  the  detent.  The  machinery  is 
thus  set  in  motion,  and  the  hammer  strikes  the  bell.  A 
single  blow  of  the  hammer  follows  each  electrical  impulse, 
and  the  motion  of  the  machinery  raises  the  lever  again  to 
its  place,  and  poises  it  on  the  keeper  ready  to  be  tripped 
for  another  blow.  If  the  number  of  the  box  is  ten  or  less, 
it  is  indicated  by  a  corresponding  number  of  strokes  on  the 
bell.  If  above  ten,  the  digits  of  the  number  are  indicated 
by  striking  the  numbers  corresponding  to  them,  with  a  short 
pause  between.  Thus,  to  strike  the  number  25,  two  blows 
would  be  given,  and  then  after  a  pause  five  more.  Num- 
bers containing  ciphers,  and  those  made  up  of  figures  re- 
peated, as  22,  33,  etc.,  are  not  used  for  the  signal-boxes. 

320.  Submarine  Lines.  — A  submarine  line  is  made  by  a 
cable.  The  core  of  the  cable  consists  of  one  wire,  or  more 
commonly  a  strand  of  several  wires,  of  copper.  This  is 
generally  covered  with  a  compound  of  gutta-percha  and 
resinous  substances,  which  fills  the  interstices  between  the 
wires.  It  is  then  included  in  one  or  more  coatings  of 
gutta-percha,  then  in  a  layer  of  tarred  yarn,  and  finally  in 
a  sheathing  of  iron  wire,  laid  on  spirally,  to  give  the  cable 
sufficient  strength  to  withstand  the  strain  of  paying  out,  or 
that  to  which  it  may  be  subjected  from  the  inequalities  of 
the  ocean  bed.  Figure  226  shows  the  construction  (full 
Fig.  226.  size)  of  the  Malta  and  Alexan- 

dria cable,  1330  nautical  miles 
long,  and  one  of  the  best  in 
operation.  O  is  a  strand  of 
seven  copper  wires,  laid  in  a 
compound  of  gutta-percha  and 
resins  ;  C,  three  layers  of  gutta- 
percha,  with  the  same  compound  between  them  ;  H,  tarred 
yarn ;  and  /,  the  eighteen  wires  of  the  sheathing.  The  di- 


ELECTRICITY.  317 

ameter  is  .85  of  an  inch.     Near  the  shore,  where  it  is  more 
exposed  to  injury,  the  sheathing  is  made  much  stronger. 

321.  Electricity  as  a  Source  of  Mechanical  Power:  —  A 
great  variety  of  electro-magnetic  machines  have  been  con- 
structed with  a  view  to  applying  electric  force  to  the  work 
now  done  by  steam.     They  all  depend  on  the  power  of  an 
electro-magnet  to  acquire  or  to  lose  its  magnetism  on  the 
passage  or  the  interruption  of  the  current ;  or  to  reverse 
its  poles  when  the  direction  of  the  current  is  changed. 

Electro-magnetic  engines  have  never  yet  been  con- 
structed of  above  eight  or  ten  horse-power,  though  there 
is  apparently  nothing  to  limit  them  to  this  low  power. 
The  great  obstacle  to  the  success  of  these  engines  is  the 
expense  of  generating  the  electricity  to  run  them.  It  costs 
some  forty  or  fifty  times  as  much  to  generate  electric  force 
as  to  generate  the  same  amount  of  steam  force.  Yet,  for 
certain  kinds  of  work,  where  rapid  motion  and  compara- 
tively little  force  are  required,  electric  engines  have  been 
found  to  answer  better  than  small  steam-engines. 

322.  Electric  Lamps.  —  Various  arrangements  have  been 
invented  for  giving  steadiness  to  the  electric  light  by  keep- 
ing the  carbon  points  within  such  a  distance  of  each  other 
that  the  current  can  pass  between  them.     Foucault,  aided 
by  Duboscq,  was  the  first  (1849)  to  construct  an  electric 
lamp  of  this  kind.     In  it,  by  means  of  an  electro-magnet 
and  of  clock-work,  the  points  are  made  to  travel  towards 
each  other  at  rates  corresponding  to  those  of  their  com- 
bustion, the  positive  pole  moving  faster  than  the  negative. 

The  electric  lamp  has  not  yet  been  used  successfully  for 
lighting  streets.  The  light  may  be  kept  up  for  hours,  but 
it  is  not  perfectly  steady,  and  the  apparatus  cannot  be 
safely  left  without  an  attendant.  It  has,  however,  been 
used  with  excellent  effect  where  a  limited  space  had  to  be 
lighted  for  a  few  nights,  as  in  building  bridges.  It  has  also 
been  used  with  success  for  light-houses,  in  England  and 


318  ELECTRICITY. 

France.     The  power  of  the  electric  light  to  penetrate  fogs 
is  found  to  be  far  superior  to  that  of  the  usual  oil  light. 


SUMMARY. 

Electro-metallurgy  is  the  art  of  depositing  a  metal  by 
electrolysis  upon  a  surface  prepared  to  receive  it.  In 
electrotyping  the  metal  deposited  is  afterwards  removed  ; 
in  electro-plating  and  gilding  it  is  made  to  adhere  per- 
manently to  the  surface.  (308  —  311.) 

The  electric  force  has  been  used  for  regulating  the 
motion  of  clocks.  (312.) 

Morse's  telegraph  depends  on  the  power  of  the  current 
to  develop  magnetism.  (314.) 

The  Combination  Printing  Telegraph  and  the  Electric 
Fire-alarm  are  other  important  forms  of  the  electro- 
magnetic telegraph.  (318-319.) 

CONCLUSION. 

We  have  now  become  somewhat  acquainted  with  that 
peculiar  mode  of  molecular  motion  which  we  denominate 
Electricity.  We  have  seen  that  it  may  be  developed  by 
chemical  action,  magnetism,  heat,  and  friction ;  and  that  it 
has  power  to  decompose  chemical  compounds,  and  to 
develop  magnetism,  heat,  and  mechanical  motion.  We 
have  also  seen  how  extensively  this  force  has  come  to  be 
applied  to  the  arts,  in  electrotyping,  electro-plating,  tele- 
graphy, and  illumination. 

This  mysterious  force,  which  we  can  generate  on  a  small 
scale  by  the  above  methods,  is  developed  on  an  enormous 
scale  in  nature  by  processes  of  which  we  know  little  or 
nothing.  The  sparks  of  our  most  powerful  electrical  ma- 
chines, and  the  most  brilliant  discharge  which  we  can 
obtain  through  a  vacuum  tube,  are  but  miniature  repre- 
sentations of  the  lightning  and  the  aurora. 


APPENDIX 


APPENDIX. 


PHYSICS    OF    THE    ATMOSPHERE. 


TEMPERATURE  OF  THE  ATMOSPHERE. 

1.  Composition   of  the  Atmosphere.  —  The  atmosphere  is  a 
gaseous  envelope  surrounding  the  earth  to  the  depth  of  about 
fifty  miles.     It  is  composed  mainly  of  a  mixture  of  nitrogen  and 
oxygen,  in  the  proportion  of  79.1  parts  of  the  former  to  20.9  of 
the  latter.     It  contains  also  a  little  carbonic  acid  and  a  vari- 
able amount  of  watery  vapor. 

2.  How  the  Air  is  Heated.  —  The  air  receives  its  heat  direct- 
ly or  indirectly  from  the  sun.     A  part  of  the  solar  rays  are  ab- 
sorbed in  passing  through  the  atmosphere.     It  thus  becomes 
warmed  directly  by  solar  radiation.     A  part  of  the  rays  fall  upon 
the  surface  of  the  earth,  which  absorbs  them,  and  thus  becomes 
heated.     This  heat  is.  then  radiated  back  again,  and  is  absorbed 
by  the  air,  which  thus  becomes  heated  by  terrestrial  radiation. 

Owing  to  the  greater  specific  heat  of  water,  the  sea  becomes 
less  heated  during  the  day  than  the  land  does.  Again,  it  is  a 
poorer  radiator  than  the  land.  Hence,  the  terrestrial  radiation 
from  the  land  is  much  greater  than  from  the  sea. 

The  watery  vapor  in  the  air  plays  an  important  part  in  this 
heating  process  ;  for,  while  it  allows  the  luminous  rays  of  the 
RP."  to  pass  readily  through  it  on  their  way  to  the  earth,  it  will 
irOt  allow  them  to  pass  back  again  when  they  are  radiated  from 
:lie  earth  as  obscure  heat.  The  sunbeams  are,  so  to  speak, 
caught  in  a  trap  from  which  they  cannot  escape. 

This  is  the  main  reason  why  it  is  warmer  at  the  base  of  a 
mountain  than  at  its  top,  where  the  solar  radiations  are  more 
powerful.  In  the  upper  regions  of  the  atmosphere  there  is  less 
watery  vapor  to  absorb  the  terrestrial  radiations. 


322  APPENDIX. 

3.  The  Daily  Variation  of  Temperature.  —  The  temperature 
is  found  to  be  greatest,  not  at  noon,  when  the  solar  radiations 
are  most  intense,  but  two  or  three  hours  later  ;  and  least,  not  at 
midnight,  but  an  hour  or  two  before  sunrise.     During  the  fore- 
noon, the  earth  receives  more  heat  than  it  radiates.     In  the  af- 
ternoon it  begins  to  receive  less  heat,  but  for  two  or  three  hours 
it  still  receives  more  than  it  radiates,  so  that  it  grows  hotter  and 
gives  out  more  heat  than  at  noon.     During  the  night,  it  receives 
no  heat  from  the  sun,  and  gives  out  less  and  less  till  about  an 
hour  before  sunrise,  when  the  heat  it  receives  from  the  return- 
ing sun  again  equals  what  it  radiates. 

4.  The  Distribution  of  Temperature  in  the  Atmosphere.  —  The 
highest  temperature  of  the  earth  is  found  to  be  in  an  irreg- 
ular belt  lying  within  the  tropics.     The  warm  belt  is  continu- 
ally shifting  its  position,  passing  northward  with  the  sun  until 
midsummer,  and  then  southward  again  until  midwinter. 

From  the  warm  belt,  the  temperature  diminishes  towards  the 
poles.  In  the  southern  hemisphere,  which  is  nearly  all  water,  it 
shades  off  gradually  and  regularly  ;  in  the  northern,  where  there 
are  large  bodies  of  land,  the  changes  are  quite  irregular.  In 
the  summer  the  atmosphere  over  the  continents  becomes  much 
hotter  than  over  the  ocean,  owing  to  the  greater  radiation  from 
the  land  ;  while  in  the  winter  the  air  over  the  continents  is  much 
colder  than  over  the  ocean,  since  the  land  has  cooled  down  fast- 
er than  the  sea. 

The  distribution  of  heat  is  further  modified  by  the  oceanic 
currents  and  the  prevailing  winds.  The  Gulf  Stream  and  the 
southwesterly  winds  keep  the  temperature  of  western  Europe 
much  above  that  of  the  eastern  coast  of  America  in  the  same 
latitude.  For  a  similar  reason,  the  western  coast  of  America  is 
warmer  than  the  eastern  coast  of  Asia. 

ATMOSPHERIC    PRESSURE. 

5.  The  Daily  Variation  of  Atmospheric  Pressure.  —  The  ob- 
servations of  the  barometer  show  two  maxima  and  two  minima 
of  atmospheric  pressure  during  the  day :  the  former  occurring 
from  nine  to  eleven  A.  M.,  and  from  nine  to  eleven  P.  M.  ;  and 
the  latter  from  three  to  five  A.  M.,  and  from  three  to  five  P.  M, 


323 

These  variations  are  much  more  marked  in  tropical  regions  than 
elsewhere.  As  the  air  in  the  hemisphere  under  the  sun's  rays 
becomes  heated,  it  expands  upwards  and  flows  over  upon  the 
other  hemisphere  where  the  air  is  colder  and  denser.  There  is 
thus  sweeping  round  the  globe,  from  day  to  day,  a  wave  of  heat, 
from  whose  crest  the  air  is  continually  flowing  towards  the  re- 
gion of  greatest  cold.  Aga\n,  the  variation  in  the  elastic  force 
of  the  watery  vapor  in  the  atmosphere  tends  to  produce  two 
maxima  and  two  minima  of  pressure  each  day.  One  maximum 
occurs  at  about  ten  A.  M.,  when  the  evaporation  is  most  rapid, 
and  the  other  a  little  before  sunset,  when  there  is  the  greatest 
amount  ofwatery  vapor  in  the  air.  One  minimum  occurs  at  about 
ten  P.  M.,  when  the  dew  is  falling  fastest,  and  the  other  a  little  be- 
fore sunrise,  when  there  is  the  least  amount  of  watery  vapor  in 
the  air.  The  effect  of  these,  combined  with  that  of  the  heat- 
wave, gives  the  two  daily  maxima  and  minima  first  mentioned. 

6.  The  Distribution  of  Atmospheric  Pressure.  —  In  general 
there  is  an  irregular  belt  of  low  pressure  within  the  tropics, 
bounded  on  each  side  by  a  broad  belt  of  high  pressure.  North 
and  south  of  these  are  other  belts  of  low  pressure,  while  about 
each  pole  there  is  probably  a  region  of  high  pressure.  The 
belts  south  of  the  equator  are  much  more  uniform  and  regular 
than  those  north  of  the  equator ;  as  may  be  seen  by  reference 
to  Map  I.  (at  the  end  of  the  book)  on  which  the  blue  lines 
represent  pressures  below  thirty  inches,  and  the  red  lines  thirty 
inches  and  above. 

In  winter  (as  shown  in  Map  II.),  the  north  polar  region  of 
low  pressure  has  two  centres  of  minimum  pressure  ;  one  in  the 
northern  Atlantic  near  Iceland,  and  the  other  in  the  northern 
Pacific.  At  the  same  time  there  is  a  broad  belt  of  high  pres- 
sure stretching  across  Asia  and  North  America,  with  a  centre  of 
maximum  pressure  on  each  continent. 

In  summer  (as  shown  in  Map  III.),  there  are  centres  of  high 
pressure  in  the  middle  of  the  northern  Atlantic  and  Pacific  ;  and 
a  broad  band  of  low  pressure  stretching  across  North  America 
and  Asia,  with  a  centre  of  minimum  pressure  on  each  continent. 

There  are  two  things  which  tend  to  diminish  the  atmospheric 
pressure  ;  high  temperature,  and  great  humidity.  High  tem- 
perature causes  the  air  to  expand,  rise,  and  flow  away  to  colder 


regions.  Great  humidity  diminishes  the  density  of  the  air. 
Humid  air  therefore  rises,  but,  in  rising,  it  becomes  cooled,  and 
a  part  of  its  moisture  is  precipitated  as  rain.  In  this  conden- 
sation a  large  amount  of  heat  is  given  out,  which  again  raises 
the  temperature  of  the  air  and  causes  it  to  expand  still  more. 

Now  in  the  tropics  there  is  an  excess  of  both  heat  and  mois- 
ture. The  air  therefore  rises  and  flows  over  towards  the  north 
and  south,  giving  rise  to  the  belt  of  low  pressure  bounded  by 
belts  of  high  pressure. 

Again,  in  the  regions  north  and  south  of  these  belts  of  low 
pressure,  the  air  is  found  to  be  highly  charged  with  moisture 
which  is  brought  thither  by  the  prevailing  winds,  and  continu- 
ally precipitated  in  rain.  Hence,  in  this  region  also,  the  air 
rises  and  flows  over  towards  the  north  and  south,  producing  a 
region  of  high  pressure  towards  the  poles  and  increasing  the 
pressure  in  the  belts  towards  the  equator. 

The  irregularity  in  the  belts  of  pressure  in  the  northern  hem- 
isphere is  due  to  the  modifying  influence  of  the  continents.  In 
the  summer,  both  North  America  and  Asia  become  excessively 
heated,  while  the  adjacent  seas  are  comparatively  cool.  Hence 
the  air  pours  over  from  the  land  to  the  sea,  giving  rise  to  low 
pressure  on  the  continents  and  high  pressure  on  the  oceans. 
The  more  completely  the  sea  is  shut  in  by  the  heated  land,  as  in 
the  northern  Atlantic,  the  greater  the  atmospheric  pressure 
upon  it.  It  is  also  this  excessive  heat  of  the  northern  conti- 
nents in  summer  which  causes  the  great  pressure  upon  the 
southern  hemisphere  at  the  same  season.  (See  Map  III.) 

In  winter  the  conditions  are  reversed.  The  land  becomes 
excessively  cold,  and  the  air  over  it  dense  and  contracted.  The 
warmer  air  from  the  sea  now  pours  over  upon  the  land,  causing 
the  high  pressure  in  North  America  and  Asia,  and  the  low 
pressure  in  the  northern  Atlantic  and  Pacific.  (See  Map  II.) 

WINDS. 

7.  Cause  of  Winds.  —  Winds  are  currents  of  air,  and  are  di- 
rectly caused  by  atmospheric  pressure.  If  two  neighboring 
regions  come  to  be  of  very  unequal  temperature,  the  lighter  air 
of  the  warmer  region  will  rise  and  flow  over  to  the  colder  region, 


APPENDIX.  325 

while  the  heavier  air  of  the  colder  region  will  flow  in  below  to 
supply  its  place.  Thus  we  always  have  a  surface  wind  blowing 
from  a  region  of  lower  temperature  and  high  pressure  towards 
one  of  higher  temperature  and  low  pressure,  and  an  upper  wind 
blowing  in  the  opposite  direction.  We  have  an  illustration  of 
this  in  the  wind  which  always  sets  in  from  every  direction  to- 
wards a  large  fire.  We  have  another  in  the  /tfw^/and  sea  breezes. 
On  the  sea-coast  a  breeze  sets  in  from  the  sea  in  the  morning. 
At  first  a  mere  breathing,  it  gradually  rises  to  a  stiff  breeze  in 
the  heat  of  the  day,  and  again  sinks  to  a  calm  towards  evening. 
Soon  after,  a  breeze  springs  up  from  the  land,  and  blows  strongly 
seaward  during  the  night,  dying  away  towards  morning,  when 
the  sea-breeze  begins  once  more.  These  breezes  are  especially 
marked  in  tropical  regions,  where  the  difference  of  temperature 
on  land  and  sea  is  greatest. 

8.  Trade-Winds.  —  While  the  air  above  is  flowing  north  and 
south  from  the  tropical  belt  of  low  pressure,  a  surface  wind  will 
set  in  from  the  region  of  high  pressure  to  supply  its  place. 
Were  the  earth  at  rest,  these  surface  winds  would  blow  directly 
from  the  north  and  south  towards  the  equator.  But  the  earth 
is  rotating  from  west  to  east,  and  objects  on  the  surface  at  the 
equator  are  carried  round  towards  the  east  at  the  rate  of  about  17 
miles  a  minute.  But  as  we  go  away  from  the  equator,  this 
velocity  diminishes,  so  that  in  latitude  60°  it  is  only  8^  miles  ? 
minute,  and  at  the  poles  it  is  nothing.  The  wind,  then,  blow 
ing  towards  the  equator,  is  continually  coming  to  places  whicl 
have  a  greater  velocity  eastward  than  itself,  and  therefore  lag; 
behind  and  appears  to  move  westward.  This,  combined  with 
its  motion  towards  the  equator,  makes  the  surface  wind  north  of 
the  equator  a  northeast  wind,  and  the  one  south  of  the  equator 
a  soiitheast  wind.  These  winds  blow  with  great  steadiness  and 
constancy,  and  from  the  service  they  render  to  commerce  are 
called  trade-winds. 

In  mid-ocean  in  the  Atlantic,  the  north  trades  prevail  between 
latitudes  9°  and  30°,  and  in  the  Pacific,  between  latitudes  9°  and 
26°  ;  and  the  south  trades  in  the  Atlantic,  between  latitudes  4° 
north  and  22°  south,  and  in  the  Pacific  between  latitudes  4° 
north  and  23^°  south.  These  limits  are,  however,  not  station- 
ary, but  follow  the  sun,  advancing  northwards  from  January  to 
June,  and  retreating  southwards  from  July  to  December. 


326  APPENDIX. 

9.  Region  of  Calms.  —  The  region  of  calms  is  a  belt  of  about 
4°  or  5°  in  breadth,  stretching  across  the  Atlantic  and  the  Pacific, 
generally  parallel  to  the  equator.     It  is  marked  by  a  lower  at- 
mospheric pressure  than  is  found  to  the  north  and  to  the  south 
of  it  in  the  regions  of  the  trade-winds.     It  is  also  characterized 
by  the  daily  occurrence  of  heavy  rains  and  severe  thunder- 
storms.    The  position  of  the  belt  varies  with  the  sun. 

There  are  two  other  regions  or  belts  of  calms  at  the  limits  of 
the  north  and  south  trades.  Except  in  the  Pacific  Ocean,  these 
belts  are  either  broken  up,  so  as  to  appear  only  in  patches,  or 
are  completely  obliterated  by  the  disturbing  influences  arising 
from  the  unequal  distribution  of  land  and  water.  Of  these  cir- 
cumscribed regions  of  calms,  the  most  interesting  is  that  marked 
out  by  the  high  pressures  in  the  North  Atlantic.  This  is  the 
region  of  the  Sargasso  Sea,  which  is  thus  characterized  not  only 
by  its  still  waters,  but  also  by  its  still  atmosphere.  A  similar 
region  of  calms  exists  in  the  South  Atlantic.  These  calms  are 
well  known  to  sailors. 

10.  Winds  in  Middle  Latitudes.  —  Surface  winds  will  flow 
from  the  belts  of  high  pressure  not  only  towards  the  equatorial 
belt  of  low  pressure,  but  also  towards  the  belts  of  low  pressure 
on  the  other  side.     These  currents  are  continually  coming  to 
places  which  have  a  less  velocity  eastward  than  their  own,  and 
therefore  appear  to  move  eastward.     This,  combined  with  their 
motion  from  the  equator,  tends  to  make  them  southwest  winds  in 
northern  latitudes  and  northwest  winds  in  southern  latitudes. 
These  are  the  prevailing  winds  in  these  regions,  as  has  been 
proved  by  a  long  series  of  observations,  but,  owing  to  various 
disturbing  causes,  they  are  much  less  uniform  and  constant  than 
the  trade-winds.     This  is  especially  true  of  the  northern  re- 
gion- 
There  will  also  be   surface  winds   blowing  from   the   poles 

towards  these  same  belts  of  low  pressure.  Of  course  there  will 
be  upper  currents  in  opposite  directions  to  all  these  surface 
winds. 

n.  Winds  of  the  Northern  Atlantic.  —  It  is  found  that  wher- 
ever there  is  a  centre  of  low  pressure  the  winds  blow  towards  it, 
not  directly,  but  spirally,  and  somewhat  to  the  right  of  it.  We 
have  an  illustration  of  this  in  the  winter  winds  of  the  northern 


APPENDIX.  327 

Atlantic,  when  there  is  a  centre  of  low  pressure  near  Iceland. 
Along  the  North  American  coast  the  prevailing  winds  are  from 
the  N.  W.  At  the  more  northern  places  the  general  direction 
is  more  northerly,  while  farther  south  it  is  more  westerly.  In 
the  Atlantic,  between  Great  Britain  and  America,  the  direction 
is  nearly  S.  W.  ;  this  is  also  nearly  the  direction  in  France,  Bel- 
gium, and  the  south  of  England.  At  Dublin,  and  in  the  south 
of  Scotland,  it  is  about  W.  S.  W.  ;  at  Copenhagen  it  is  S.  S.  W. ; 
at  St.  Petersburg  it  is  nearly  S. ;  and  at  Hammerfest,  near  the 
North  Cape  in  Norway,  it  is  S.  S.  E.  We  thus  see  that  the 
whole  atmosphere  flows  in  towards  arid  upon  the  region  of  low 
pressure  round  Iceland, — not  directly  towards  the  region  of 
lowest  pressure,  but  in  a  direction  a  little  to  the  right  of  it.  We 
can  now  understand  why  it  is  that  the  prevailing  winds  in  North 
America  at  this  season  are  N.  W.,  while  in  Greenland  and  in 
Great  Britain  a  N.  W.  wind  is  scarcely  known. 

It  is  mainly  to  this  low  pressure  which  draws  over  Great 
Britain  the  S.  W.  winds  from  the  warm  waters  of  the  Atlantic, 
that  this  island  owes  its  mild,  open,  and  rainy  winters.  It  is 
the  same  pressure  which  gives  Russia  and  Central  Europe  their 
severe  winters,  since  on  account  of  it  a  slow,  steady  air-current 
from  the  cold  regions  of  Northern  Asia  is  drawn  westward  over 
those  parts  of  Europe.  Finally,  the  same  low  pressure  draws 
over  British  America  and  the  United  States,  by  the  N.  W.  wind, 
the  cold,  dry  currents  of  the  polar  regions.  In  the  State  of 
Maine  the  mean  January  temperature  is  about  23°,  whilst  on 
the  coast  of  England,  10°  farther  north,  it  is  as  high  as  40". 

12.  Winds  of  Asia  and  North  America. —  It  will  be  seen, 
from  the  position  of  the  centres  of  high  and  low  pressure,  that 
in  winter  the  general  direction  of  the  winds  must  be  outward 
from  the  continents  of  North  America  and  Asia  ;  while  in  sum- 
mer it  is  inward.     Thus,  in  winter,  the  prevailing  wind  of  New 
England  is  N.  W. ;  in  Texas,  N.  ;  and  in  Oregon,  S.  E.    In  sum- 
mer, the  prevailing  winds  in  Oregon  are  N.  W.  ;  in  Texas,  S. ; 
and  on  the  eastern  coast  of  the  United  States,  S.  and  S.  W. 
In  Asia  these  regular  changes  in  the  direction  of  the  winds  are 
even  more  marked. 

13.  Monsoons.  —  The  term  monsoon,  derived  from  the  Arabic 
word  mausim^  a  set  time  or  season  of  the  year,  has  been  long 


328  APPENDIX. 

applied  to  the  prevailing  winds  in  the  Indian  Ocean,  which  blow 
from  the  S.  W.  from  April  to  October,  and  from  the  N.  E.,  or 
opposite  direction,  from  October  to  April.  During  the  sum- 
mer, when  the  sun  is  north  of  the  equator,  the  continent  oi 
Asia  becomes  heated  to  a  much  greater  degree  than  the  Indian 
Ocean,  which  in  its  turn  is  warmer  than  Australia  and  South 
Africa.  Hence,  as  the  heated  air  of  Southern  Asia  expands  and 
rises,  and  the  pressure  is  thereby  reduced  nearly  half  an  inch 
below  the  average,  colder  air  from  the  S.  flows  in  to  take  its 
place,  and  thus  a  general  movement  of  the  atmosphere  of  the 
Indian  Ocean  sets  in  towards  the  N.,  giving  a  southerly  direc- 
tion to  the  wind.  But  as  the  wind  comes  from  parts  of  the 
globe  which  revolve  quicker  to  those  which  revolve  more  slowly, 
it  gets  a  westerly  direction.  The  combination  of  these  two  di- 
rections results  in  the  S.  W.  monsoon,  which  accordingly  pre- 
vails there  in  summer.  Since,  during  winter,  when  the  sun  is 
south  of  the  equator,  Asia  is  colder  than  the  Indian  Ocean,  and 
the  pressure  is  thereby  increased  nearly  half  an  inch  above  the 
average,  a  general  movement  of  the  atmosphere  sets  in  towards 
the  S.  and  W.  As  this  is  the  same  direction  as  the  ordinary 
trade-wind,  the  result  during  winter  is  not  to  change  the  direc- 
tion of  that  wind,  but  only  to  increase  its  velocity.  Thus,  south- 
ward of  the  equator,  owing  to  the  absence  of  large  tracts  of 
land,  the  S.  E.  trades  prevail  throughout  the  year ;  while  north 
of  the  equator,  in  the  east, we  find  the  S.  W.  monsoon  in  sum- 
mer and  the  N.  E.  in  winter.  It  is  only  in  summer  and  north 
of  the  equator  that  great  changes  are  effected  in  the  direction 
of  the  trade-winds. 

Similar,  though  less  strongly  marked  monsoons  prevail  off 
the  coasts  of  Upper  Guinea  in  Africa,  and  Mexico  in  America. 


STORMS. 

14.  Storms.  —  We  have  now  considered  the  general  atmos- 
pheric disturbances  caused  by  the  accumulation  of  heat  and 
moisture  in  the  air  over  large  regions  of  the  globe.  In  addi- 
tion to  these  general  disturbances  there  are  local  disturbances  of 
the  same  kind,  called  storms.  When  the  air  over  any  consider- 
able tract  becomes  excessively  heated  and  humid,  it  rises  and 


APPENDIX.  329 

overflows,  producing  a  local  centre  of  minimum  pressure.  Sur- 
face winds  set  in  towards  this  centre  from  all  sides  in  a  spiral 
direction  ;  as  the  humid  air  rises  it  becomes  cooled,  and  its 
moisture  is  precipitated  as  rain  or  snow.  A  large  amount  of 
heat  is  thus  set  free,  which  causes  the  air  to  expand  still  more. 
Sometimes  these  storms  remain  stationary,  but  they  generally 
move  forward  in  an  easterly  direction. 

The  storms  of  North  America  usually  have  their  rise  in  the 
region  east  of  the  Rocky  Mountains,  travel  eastward  towards  the 
coast,  and  cross  the  Atlantic.  They  are  preceded  by  a  high 
temperature  and  a  moist  air,  and  followed  by  a  low  temperature 
and  a  dry  air.  When  the  storm  is  approaching,  the  wind  sets 
in  from  the  east,  and  there  is  usually  the  heaviest  fall  of  rain  be- 
fore the  centre  of  the  storm  arrives.  In  this  centre  there  is 
usually  a  calm,  and  often  considerable  clear  sky.  As  the  centre 
passes,  the  wind  suddenly  veers  round  to  the  west,  and  a  short, 
heavy  fall  of  rain  follows  ;  the  temperature  rapidly  falls,  and  the 
barometer  rapidly  rises.  When  the  centre  of  the  storm  passes 
to  the  north,  the  wind  sets  in  from  the  southeast,  and  veers 
round  by  the  south  to  the  southwest.  When  the  centre  of  the 
storm  passes  to  the  south,  the  wind  sets  in  from  the  northeast, 
and  veers  round  by  the  north  to  the  northwest. 

When  a  great  storm  begins  near  the  Mississippi,  the  wind  at 
St.  Louis  will  be  easterly,  while  farther  east  it  will  be  westerly. 
This  easterly  wind  travels  eastward  with  the  storm  ;  that  is,  in 
a  direction  opposite  to  that  in  which  it  blows.  The  westerly 
wind  which  follows  the  storm  travels  along  with  it ;  that  is,  in 
the  same  direction  as  that  in  which  it  blows. 

The  storms  of  America  are  usually  very  long  in  a  north  and 
south  direction,  and  travel  side  foremost ;  while  the  storms  of 
Europe  are  either  circular  or  slightly  oblong  in  the  direction  of 
their  motion.  The  latter  are  followed  by  less  depression  of 
temperature  than  those  of  America. 

Tornadoes  are  very  violent  storms,  usually  of  small  dimen- 
sions. Here,  as  in  other  storms,  the  wind  sets  in  spirally 
towards  the  region  of  minimum  pressure,  which  is  also  the 
centre  of  the  storm. 

15.  Whirlwinds.  —  Whirlwinds  are  in  several  respects  very 
different  from  the  storms  already  described.  They  seldom  last 


330 


APPENDIX. 


longer  than  a  minute,  sometimes  only  a  few  seconds  ;  their 
breadth  varies  from  twenty  to  a  few  hundred  yards  ;  their  course 
seldom  exceeds  25  miles  in  length  ;  and  while  they  last  the 
changes  of  the  wind  are  sudden  and  violent.  The  direction  of 
the  eddy  of  the  whirlwind,  especially  when  of  small  diameter, 
differs  from  the  rotation  of  the  winds  in  a  storm,  in  the  fact  that 
it  is  not  uniform,  but  depends  on  the  direction  of  the  stronger 
of  the  two  winds  which  give  rise  to  it.  Thus,  suppose  a  whirl- 
wind be  produced  by  the  rushing  of  a  north  wind  against  a 
south  wind,  then,  if  the  north  wind  be  the  stronger  and  on  the 
west,  the  whirl  will  be  in  the  direction  of  the  hands  of  a  watch, 
but  if  the  south  wind  be  the  stronger  the  eddy  will  turn  in  the 
opposite  direction. 

Whirlwinds  are  often  originated  in  the  tropics  during  the  hot 
season,  especially  in  flat,  sandy  deserts,  which,  becoming  un- 
equally heated  by  the  sun,  give  rise  to  numerous  ascending  col- 
umns of  air.  In  their  contact  with  each  other,  these  ascending 
currents  give  rise  to  eddies,  thus  producing  whirlwinds  which 
carry  up  with  them  clouds  of  dust.  Of  this  description  are  the 
dust-whirlwinds  of  India,  illustrated  in  Figures  227  and  228. 

Fig.  227. 


The  large  arrows  in  Figure  228  show  the  rotation  of  the  whole 
whirlwind  round  its  axis,  while  the  small  arrows  show  the  rota- 


APPENDIX. 


331 


tion  of  each  column  round  its  own  axis.  Figure  227  shows  the 
general  appearance  of  a  dust-whirlwind  as  seen  from  a  distance. 
A  dust-storm  is  caused  by  a  number  of  whirlwind  columns  moving 
together  over  the  earth.  The  storm  generally  comes  on  with- 

Fig.  228. 


^PJ<f^  0^<?i^J^ 

'^'1^3^jMfe3 


out  warning  from  any  direction,  and  the  barometer  is  said  not  to 
be  perceptibly  aifected  by  it.  A  low  bank  of  dark  cloud  is  seen 
in  the  horizon,  which  rapidly  increases,  and,  before  the  specta- 
tor is  aware,  the  storm  bursts  upon  him,  wrapping  everything 
in  midnight  darkness.  An  enormous  quantity  of  dust  is  whirled 
aloft,  which  is  sometimes  broken  into  distinct  columns,  each 
whirling  on  its  axis.  Violent  gusts  or  squalls  succeed  each 
other  at  intervals,  which  gradually  become  weaker,  and  at  the 
close  of  the  storm  a  fall  of  rain  generally  takes  place.  The  air 
is  often  highly  electrical,  arising  probably  from  the  friction  of 
the  dust-laden  currents  against  each  other.  The  Simoom  may 
be  regarded  as  in  part  a  whirlwind  or  a  succession  of  whirl- 
winds of  this  description.  Sir  S.  W.  Baker  thus  graphically 


332  APPENDIX. 

describes  the  behavior  of  the  dust- whirlwinds  which  occur  in 
Nubia  in  April,  May,  and  June: — "I  have  frequently  seen 
many  such  columns  at  the  same  time  in  the  boundless  desert, 
all  travelling  or  waltzing  in  various  directions,  at  the  fitful 
choice  of  each  whirlwind;  this  vagrancy  of  character  is  an 
undoubted  proof  to  the  Arab  mind  of  their  independent  and 
diabolical  character." 

Extensive  fires,  such  as  the  burning  of  the  prairies  in  Ameri- 
ca, and  volcanic  eruptions,  also  cause  whirlwinds  by  the  up- 
ward currents  produced  by  the  heated  air  ;  and  these,  as  well 
as  the  other  whirlwinds  already  mentioned,  are  occasionally 
accompanied  with  rain  and  electrical  displays. 

16.  Waterspouts.  —  Waterspouts   are  whirlwinds   occurring 
over  the  sea  or  over  sheets  of  fresh  water.     When  fully  formed 
they  appear  as  tall  pillars  stretching  from  the  sea  upward  to  the 
clouds,  and  exhibiting  the  same  whirling  motion  round  their 
axes,  and  the  same  progressive  movement  of  the  mass,  as  the 
dust-whirlwinds.     As  they  consist  of  vortices  of  wind  in  rapid 
motion,  the  sea  is  tossed  into  violent  agitation  round  their  bases 
as  they  career  onwards.     The  danger  arising  from  them  consists 
in  the  enormous  velocity  of  the  wind,  and  the  sudden  changes 
in  its  direction  experienced  by  ships  which  encounter  them.     It 
is  a  popular  fallacy  that  the  water  of  the  sea  is  sucked  up  by 
them,  it  being  only  the  spray  from  the  broken  waves   that  is 
carried  up  by  the  whirling  vortex.     This  is  conclusively  proved 
by  the  fact  that  the  water  poured  down  on  the  decks  of  ves- 
sels by  waterspouts  is  either  fresh  or  only  slightly  brackish. 

THE  MOISTURE   OF  THE    ATMOSPHERE. 

17.  The  Two  Atmospheres  of  Air  and  Vapor,  —  The  gaseous 
envelope  surrounding  the  earth  may  be  considered  as  composed 
of  two  distinct  atmospheres,  —  an  atmosphere  of  dry  air,  and 
an  atmosphere  of  vapor.     The  dry  air  is  always  a  gas,  and  its 
quantity  is  constant  from  year  to  year ;  but  the  vapor  of  water 
does  not  always  remain  in  the  gaseous  state,  and  the  quantity 
present  in  the  atmosphere  is,  by  the  processes  of  evaporation 
and  condensation,  varying  every  instant. 

1 8.  Evaporation. —  Vapor  is  continually  passing  into  the  air 


APPENDIX.  333 

from  the  surface  of  water  and  moist  bodies  at  all  temperatures 
by  the  silent  process  of  evaporation.  Evaporation  also  takes 
place  from  the  surface  of  snow  and  ice.  By  the  increase  of 
temperature  the  elastic  force  of  the  vapor  in  the  atmosphere 
is  increased,  and  with  it  the  rate  of  evaporation.  The  atmos- 
phere can  contain  only  a  certain  amount  of  vapor,  according  to 
the  temperature  ;  hence,  when  it  is  saturated  with  moisture, 
evaporation  ceases.  Conversely,  evaporation  will  be  greatest 
when  the  air  is  perfectly  free  from  vapor.  Since  atmospheric 
currents  remove  the  saturated  air  and  substitute  dry  air,  evapo- 
ration is  much  more  rapid  in  windy  than  in  calm  weather. 
Though  the  quantity  of  vapor  required  to  saturate  a  given 
space  is  the  same,  whether  it  be  filled  with  air  or  be  a  vacuum, 
yet  the  time  taken  to  saturate  it  increases  with  the  pressure  on 
the  surface  of  the  liquid.  When  water  evaporates  into  a  vacu- 
um, the  maximum  density  of  the  vapor  is  acquired  at  once  ; 
but  when  it  evaporates  into  air,  it  is  not  acquired  till  some  time 
has  elapsed.  And  since  every  addition  to  the  vapor  increases 
the  pressure,  the  rate  of  evaporation  is,  under  these  circum- 
stances, continually  diminishing. 

19.  Loss  of  Heat  by  Evaporation. —  We  have  learned  (217) 
that  when  a  liquid  passes  into  the  gaseous  form,  a  large  quan- 
tity of  heat  becomes  latent;  and  that  this  heat  becomes  sensi- 
ble again  when  the  vapor  returns  to  the  liquid  state.  The  ocean 
loses  more  heat  from  evaporation  than  the  land,  because  the 
quantity  evaporated  from  its  surface  is  much  greater.  Again, 
since  more  rain  falls  on  land  than  on  sea,  especially  in  hilly  and 
mountainous  countries,  the  temperature  of  the  air  over  the  land 
will  be  still  further  raised  by  the  heat  thus  given  out.  This  is 
one  of  the  reasons  why  the  mean  temperature  of  the  northern 
hemisphere  is  higher  than  that  of  the  southern. 

It  is  for  this  reason  that  the  sensible  temperature  depends 
on  the  humidity  of  the  air.  Dry  air  promotes  evaporation  from 
the  surface  of  the  body,  and  seems  cold ;  while  moist  air  im- 
pedes this  evaporation,  and  seems  warm.  When  the  air  is  both 
hot  and  moist,  as  in  the  dog-days,  it  is  peculiarly  oppressive. 
It  is  because  the  winds  promote  evaporation  that  the  air  seems 
cooler  on  a  windy  day  than  on  a  still  one,  though  the  tempera- 
ture may  be  the  same. 


334  APPENDIXc 

20.  Effect  of  Drainage  on  the  Temperature  of  the  Soil.' —  The- 
ory would  lead  us  to  suppose  that  drained  land  would  have  a 
higher  temperature  than  undrained  land,  because,  being  drier, 
it  loses  less  heat  by  evaporation  ;  and  experiments  have  con- 
firmed this. 

21.  Dew.  —  After  the  sun  has  set,  the  earth  is  continually 
radiating  heat   into   space,  and   is  receiving  little  or  none  in 
return.     As  it  cools  down,  it  cools  the  layer  of  air  nearest  to  it, 
and  causes  it  to  deposit  its  moisture  in  the  form  of  dew.    In  the 
same  way,  in  hot  weather,  moisture  collects  on  the  outside  of  a 
pitcher  of  ice-water.     The  cold  surface  of  the  pitcher  cools  the 
air  nearest  it  so  much  that  it  compels  it  to  give  up  a  part  of  its 
moisture. 

Every  one  has  noticed  that  dew  collects  on  some  substances 
more  readily  than  on  others.  This  is  because  they  are  better 
radiators,  and  therefore  cool  sooner. 

Dew  does  not  collect  on  a  cloudy  night,  or  under  a  roof  or 
shed,  because  the  heat  is  sent  back  by  the  clouds  and  the  roof 
as  fast  as  it  is  radiated  from  the  earth. 

There  is  no  dew  on  a  very  windy  night,  because  the  layer  of 
air  near  the  earth  is  continually  changing,  and  does  not  become 
cool  enough  to  give  up  its  moisture. 

22.  Dew-point.  —  The   ascertaining  of  the  dew-point  is   of 
great  practical  importance,  particularly  to  horticulturists,  since 
it  shows  the  point  near  which  the  temperature  during  the  night 
will  cease  to  fall.     For  when  the  air  has  been  cooled  down  by 
radiation  to  this  point,  dew  is  deposited,  heat  is  given  out,  and 
the  temperature  of  the  air  rises.     But  as  the  cooling  by  radia- 
tion proceeds,  the  air  again  falls  to,  or  slightly  under,  the  dew- 
point  ;  dew  is  now  again  deposited,  heat  liberated,  and  the  tem- 
perature raised.     Thus  the  temperature  of  the  air  in  contact 
with  plants  and  other  radiating  surfaces  may  be  considered  as 
gently  oscillating  about  the  dew-point.     For  if  it  rises  higher, 
the  loss  of  heat  by  radiation   speedily  lowers  it,  and  if  it  falls 
lower  by  ever  so  little,  the  heat  liberated  by  the  formation  of 
dew  as  speedily  raises  it.     The  dew-point,  then,  determines  the 
minimum  temperature  of  the  night ;  and  if  this  point  be  found 
by  means  of  the  hygrodeik  (256),  the  approach  of  low  temper- 
ature or  of  frost  may  be  foreseen  and  provided  against. 


APPENDIX.  33£ 

23.  Elastic  Force  of  Vapor.  — In  an  atmosphere  of  pure  steam, 
its  force  at  the  earth's  surface  is  the  pressure  it  exerts  ;   and  in 
an  atmosphere  of  vapor  and  air  perfectly  mixed,  the  elastic  force 
of  each  at  the  surface  of  the  earth   is  the   pressure  of  each. 
Hence  the  elastic  force  of  watery  vapor  would  be  the  pressure 
of  the  whole  vapor  in  the  atmosphere  over  the  place  of  obser- 
vation.    This  is  expresssed  in  inches  of  mercury  of  the  baro- 
metric column.     It  is  greatest  within  the  tropics,  and  diminishes 
towards  the  poles.     It  is  greater  in  the  atmosphere  over  the 
oceans,  and  decreases  as  we  advance  inland.     It  is  greater  in 
summer  than  in  winter,  and  greater  at  midday  than  in  the  morn- 
ing.    It  also  diminishes  with  the  height,  but  the  average  rate  at 
which  it  diminishes  is  not  known.    Balloon  ascents  have  thrown 
some  light  on  the  question,  but  the  observations  are  far  too  few 
for  determining  the  mean  rate  of  the  decrease.     The  chief  point 
established  is,  that  the  decrease  is  generally  very  far  from  uni- 
form. 

MISTS,    FOGS,   AND    CLOUDS. 

24.  Mists  and  Fogs.  —  Mists   and  fogs   are   visible   vapors 
floating  in  the  air  near  the  surface  of  the  earth.     They  are  pro- 
duced in  various  ways,  —  by  the  mixing  of  cold  air  with  air  that 
is  warm  and  moist,  or  generally  by  whatever  tends  to  lower  the 
temperature  of  the  air  below  the  dew-point. 

During  a  calm,  clear  night,  when  the  air  over  a  level  country 
has  been  cooled  by  radiation,  and  dew  begun  to  be  deposited, 
the  portion  of  the  air  in  contact  with  the  ground  is  lowered  to 
the  dew-point,  and  thus  becomes  colder  than  the  air  above  it. 
Since  there  is  nothing  to  disturb  the  equilibrium  and  give  rise 
to  currents  of  air,  and  no  cause  in  operation  which  can  reduce 
the  temperature  much  below  the  point  of  saturation,  the  air 
within  a  few  feet  of  the  surface  remains  free  from  mist  or  fog. 
But  if  the  ground  slopes,  the  cold  air,  being  heavier,  must  neces- 
sarily flow  down  and  fill  the  lower  grounds  ;  and  since  it  is 
colder  than  the  saturated  air  which  it  meets  with  in  its  course, 
it  will  reduce  its  temperature  considerably  below  the  point  of 
saturation,  and  thus  produce  mist,  or  radiation  fog,  as  it  is  some- 
times termed.  When  a  lake,  river,  or  marsh  fills  up  the  valley, 
the  air  may  become  re-saturated,  giving  rise  to  denser  fogs. 


336  APPENDIX. 

On  the  other  hand>  when  the  low  grounds  are  sandy  or  dry, 
mist  is  less  frequently  produced. 

When  an  oceanic  current  meets  a  shoal  in  its  course,  the 
cold  water  of  the  lower  depths  is  brought  to  the  surface,  and  in 
all  cases  where  its  temperature  is  lower  than  the  dew-point  of 
the  air,  fogs  are  formed  over  the  shoal.  For  a  similar  reason 
icebergs  are  frequently  enveloped  in  fogs.  In  like  manner  mist 
is  sometimes  seen  to  rise  from  rivers  whose  temperature  'is 
lower  than  that  of  the  air.  Thus  the  waters  of  the  Swiss  rivers 
which  issue  from  the  cold  glaciers  cool  the  air  in  contact  with 
them  below  the  point  of  saturation,  and  mist  is  thereby  often 
produced.  So,  also,  such  rivers  as  the  Mississippi,  which  flow 
directly  into  warmer  latitudes,  and  are  therefore  colder  than  the 
air  above  them,  are  often  covered  with  mist  or  fogs. 

When  rivers  are  considerably  warmer  than  the  air,  they  give 
rise  to  fogs,  because  the  more  rapid  evaporation  from  the  warm 
water  pours  more  vapor  into  the  atmosphere  than  it  can  hold, 
and  the  surplus  is  condensed  into  mist  by  the  colder  air  through 
which  it  rises.  Thus  deep  lakes,  and  rivers  flowing  out  of  them, 
are  in  winter  generally  much  warmer  than  the  air,  and  hence 
when  the  air  is  cold  and  its  humidity  great  they  are  covered 
with  fogs.  When  Sir  Humphrey  Davy  descended  the  Danube 
in  1818,  he  observed  that  mist  was  always  formed  during  the 
night,  when  the  temperature  of  the  air  on  shore  was  from  3°  to 
6°  lower  than  that  of  the  stream  ;  but  when  the  sun  rose,  and 
the  temperatures  became  equal,  the  mist  rapidly  disappeared. 

The  densest  fogs  occur  during  the  cold  months  in  large  towns 
built  on  rivers,  —  the  causes  which  produce  fogs  being  then  at 
the  maximum.  The  peculiar  denseness  of  the  London  Novem- 
ber fogs  is  caused  by  the  warmth  of  the  river-bed,  and  it  is  in- 
creased by  the  sources  of  artificial  heat  which  London  affords  ; 
and  since  the  temperature  is  falling  everywhere,  and  the  humid- 
ity is  then  great,  the  vapor  of  the  atmosphere  is  quickly  and 
copiously  condensed  by  the  gently  flowing  cold  easterly  winds 
which  generally  prevail  in  November. 

In  all  these  cases  the  fogs  are  confined  to  the  basin  of  the 
river  or  lake  where  they  are  formed,  and  do  not  extend  far  up 
into  the  atmosphere.  There  are,  however,  other  fogs  that 
spread  over  large  districts,  like  the  fogs  which  often  accompa- 


APPENDIX.  337 

ny  the  breaking  up  of  frosts  in  winter.  When  the  humid  south- 
west wind  has  gained  the  ascendency,  and  is  now  advancing 
over  the  earth's  surface  as  a  "  light  air,"  it  is  chilled  by  contact 
with  the  cold  ground,  and  its  abundant  vapor  thereby  condensed 
into  a  wide-spread  mist. 

Mountains  are  frequently  covered  with  mist.  Since  the  pres- 
sure and  consequently  the  temperature  of  the  air  falls  with  the 
height,  it  follows  that  as  warm  air  is  driven  up  the  slopes  of  the 
mountain  by  the  wind,  it  becomes  gradually  colder,  and  its  ca- 
pacity for  moisture  is  diminished  until  condensation  takes  place, 
and  the  mountain  is  swathed  in  mist.  Mists  often  appear  sooner 
on  the  parts  of  hills  covered  with  trees  than  elsewhere.  This 
happens  especially  when  the  mist  begins  to  form  after  midday, 
because  then  the  temperature  of  the  trees  is  lower  than  that  of 
the  grassy  slopes.  Mists  also  linger  longer  over  forests,  proba- 
bly on  account  of  the  increased  cold  arising  from  the  large  ex- 
tent of  evaporating  surface  presented  by  their  leaves  when 
drenched  with  mist.  Occasionally  the  summit  of  a  hill  or  an 
isolated  peak  is  wrapped  in  mist,  while  elsewhere  the  atmos- 
phere is  clear ;  and  though  a  breeze  be  blowing  over  the  hill, 
still 

"  Overhead 
The  light  cloud  smoulders  on  the  summer  crag," 

apparently  motionless  and  unchanged.  This  phenomenon  is 
easily  explained.  The  temperature  at  the  top  is  below  the  dew- 
point  of  the  atmospheric  current.  Hence  when  the  air  rises  to 
this  region  its  moisture  is  condensed  into  mist,  which  is  borne 
forward  over  the  top  of  the  hill  and  down  the  other  side,  acquir- 
ing heat  as  it  descends,  till  it  is  again  dissolved  and  disappears. 
Meanwhile  its  place  is  constantly  supplied  by  fresh  condensa- 
tions which  take  place  as  the  current,  rising  to  the  height  of  the 
mist,  falls  below  the  temperature  of  saturation.  Thus,  though 
the  mist  on  the  top  of  the  hill  appears  to  remain  motionless  aad 
unchanged,  the  watery  particles  of  which  it  is  composed  are  con- 
tinually undergoing  renewal. 

25.  Clouds.  —  Clouds  are  visible  vapors  floating  in  the  air  at 
a  considerable  height ;  thus  differing  from  mists  and  fogs, 
which  float  near  the  surface.  Both  arise  from  the  same  causes. 

During  the  warmest  part  of  the  day,  when  evaporation  is 
'5  V 


338  APPENDIX. 

greatest,  warm,  moist  air-currents  are  constantly  ascending  from 
the  earth.  As  they  rise  in  succession,  the  moist  air  is  pushed 
high  up  into  the  atmosphere,  and,  losing  heat  by  expansion,  a 
point  is  at  length  reached  when  it  can  no  longer  retain  the 
moisture  with  which  it  is  charged  ;  hence  condensation  takes 
place,  and  a  cloud  is  formed,  which  increases  in  bulk  as  long  as 
the  air  continues  to  ascend.  But  as  the  day  declines,  and  evap- 
oration is  checked,  the  ascending  current  ceases,  and,  the  tem- 
perature falling  from  the  earth's  surface  upwards,  the  lower 
stratum  of  air  contracts,  and  consequently  the  whole  mass  of 
dir  begins  to  descend,  and  the  clouds  are  then  dissolved  by  the 
warmth  they  acquire  in  falling  to  lower  levels.  The  whole  of 
Jhis  process  is  frequently  seen  on  a  warm  summer  day.  In  the 
morning  the  sky  is  cloudless,  or  nearly  so  ;  as  the*  heat  becomes 
greater,  clouds  begin  to  form  before  noon  and  gradually  increase 
in  numbers  and  size  ;  but,  as  the  heat  diminishes,  they  contract 
their  dimensions,  and  gather  round  the  setting  sun,  lit  up  with 
the  fiery  splendors  of  his  beams.  In  a  short  time  they  disap- 
pear, and  the  stars  come  out,  shining  in  a  cloudless  sky. 

Balloon  ascents,  as  well  as  observations  of  the  clouds,  have 
shown  that  the  whole  atmosphere,  to  a  great  height,  is  constantly 
traversed  by  many  aerial  currents,  one  above  another,  and  flow- 
ing in  different  and  frequently  in  opposite  directions.  Masses 
of  air  of  different  temperatures  thus  frequently  combine  togeth- 
er ;  and  since  the  several  portions  when  mingled  cannot  hold 
the  same  quantity  of  vapor  that  each  could  retain  before  they 
were  united,  the  excess  is  condensed  and  appears  as  cloud. 

But  again,  when  a  dry  and  heavy  wind  begins  to  set  in,  or 
take  the  place  of  a  moist  and  light  wind,  it  generally  does  so  by 
edging  itself  beneath  the  moist  wind  and  forcing  it,  as  with  a 
wedge,  into  the  upper  regions  of  the  atmosphere,  where  con- 
densation rapidly  follows,  and  dense  black  clouds,  often  heavily 
charged  with  rain,  are  formed.  This  is  a  frequent  cause  of 
cloud  and  rain  in  Great  Britain,  when  the  cold,  heavy  east  wind, 
or  polar  current,  thrusts  high  up  into  the  air  the  rain-bring- 
ing southwest  wind,  causing  it  to  darken  the  sky  and  pour 
its  surplus  moisture  in  torrents  of  rain. 

Currents  of  air  driven  up  the  sloping  sides  of  hills  and  moun 
tains  by  the  winds  often  cause  the  formation  of  clouds  (24). 


APPENDIX.  339 

26.  How  Clouds  are  suspended  in  the  Air.  —  The  example  of 
a  cloud  appearing  to  rest  on  the  top  of  a  hill  though  a  strong 
wind  be  blowing  at  the  time  (24)  suggests  how  clouds  are  sus- 
pended in  the  air.     The  cloud  itself  may  appear  stationary  or 
suspended,  but  the  particles  of  which  it  is  composed  are  under- 
going constant  renewal  or  change.     The  particles  are  upheld 
by  the  force  of  the  ascending  current  in  which  they  are  formed  ; 
but  when  that  current  ceases  to  rise,  or  when  they  become  sep- 
arated from  it,  they  begin  to  fall  through  the  air  by  their  own 
weight,  till  they  melt  away  and  are  dissolved  in  the  higher  tem- 
perature into  which  they  fall.     Hence,  as  Espy  has  reasoned, 
every  cloud  is  either  a  forming  cloud  or  a  dissolving  cloud. 
While  it  is  connected  with  an  ascending  current,  it  increases  in 
size,  is  dense  at  the  top,  and  well  defined  in  its  outlines  ;  but 
when  the  ascending  current  ceases,  the  cloud  diminishes  in  size 
and  density. 

When  a  cloud  overspreads  the  sky,  its  lower  surface  is  for 
the  most  part  horizontal,  or  more  generally  it  seems  as  if  it  was 
an  impression  taken  from  the  contour  of  the  earth's  surface 
beneath  it.  This  arises  from  the  high  temperature  of  the  air 
below  the  cloud,  which  is  sufficient  to  dissolve  the  particles  as 
they  descend  below  its  level. 

27.  Classification  of  Clouds.  —  Clouds  are  divided  into  seven 
kinds  ;    three  being  simple,  the  cirrus,  the  cumulus,  and  the 
stratus ;  and  four  intermediate  or  compound,  the  cirro-cumulus, 
the  cirro-stratus,  the  cumulo-stratus,  and  the  cumulo-cirro-stra- 
tus  or  nimbus. 

These  forms  of  clouds,  with  the  exception  of  the  nimbus, 
are  represented  in  the  plate  on  page  341.  The  one  marked 
by  one  bird  is  the  cirrus ;  by  two  birds,  the  cirro-cumulus ;  by 
three,  the  cirro-stratus;  by  four,  the  cumulus;  by  five,  the 
cumulo-stratus ;  by  six,  the  stratus. 

28.  Cirrus  Cloud. — The  cirrus  (or  curl)  cloud  consists  of 
parallel,  wavy,  or  diverging  fibres  which  may  increase  in  any  or 
in  all  directions.     Of  all  clouds  it  has  the  least  density,   the 
greatest  elevation,  and  the  greatest  variety  of  extent  and  direc- 
tion, or  figure.     It  is  the  cloud  first  seen  after  serene  weather, 
appearing  as  slender  filaments  stretching  like  white  lines  pen- 
cilled across  the  blue  sky,  and  thence  propagated  in  one  or 


340  APPENDIX. 

more  directions,  laterally,  or  upward,  or  downward.  Sometimes 
the  thin  lines  of  cloud  are  arranged  parallel  to  each  other,  the 
lines  lying  in  the  northern  hemisphere  from  north  to  south,  or 
from  southwest  to  northeast;  sometimes  they  diverge  from 
each  other  in  the  form  of  the  tail  of  a  horse  ;  while  at  other 
times  they  cross  each  other  in  different  ways,  like  rich,  delicate 
lace-work.  It  is  probable  that  the  fine  particles  of  which  this 
cloud  is  composed  are  minute  crystals  of  ice  or  snow-flakes. 
The  duration  of  the  cirrus  varies  from  a  few  minutes  to  many 
hours.  It  remains  for  a  short  time  when  formed  in  the  lower 
parts  of  the  atmosphere  and  near  other  clouds,  and  longest  when 
it  appears  alone  in  the  sky,  and  at  a  great  height. 

The  cirrus,  though  apparently  motionless,  is  closely  connect- 
ed with  the  movements  of  the  great  atmospheric  currents,  and 
is  therefore  a  most  valuable  prognostic  of  stormy  weather. 

29.  Cumulus.  —  This  name  is  applied  to  convex  or  conical 
heaps   of  clouds  increasing   upwards  from   a  horizontal  base. 
They  are  usually  of  a  very  dense  structure  ;  are  formed  in  the 
lower  regions  of  the  atmosphere  ;  and  are  carried  along  in  the 
current  next  the  earth.     The  cumulus  has  been  well  called  the 
cloud  of  the  day,  being  caused  by  the  ascending  currents  of 
warm  air  which  rise  from  the  heated  ground.     Its  beginning  is 
the  little  cloud  not  bigger  than  a  man's  hand,  which  is  the  nu- 
cleus  round  which  it  increases.     The   lower  surface  remains 
roughly  horizontal,  while  the  upper  rises  into  towering  heaps, 
which  may  continue  comparatively  small,  or  swell  into  a  size  far 
exceeding  that  of  mountains. 

When  these  clouds  are  of  moderate  height  and  size,  of  a  well- 
defined  curved  outline,  and  appear  only  during  the  heat  of  the 
day,  they  indicate  a  continuance  of  fair  weather.  But  when 
they  increase  with  great  rapidity,  sink  down  into  the  lower  parts 
of  the  atmosphere,  and  do  not  disappear  towards  evening,  rain 
may  be  expected.  If  loose  fleecy  patches  of  cloud  begin  to  ap- 
pear thrown  out  from  their  surfaces,  the  rain  is  near  at  hand. 

30.  Stratus.  —  The  stratus,  as  its  name  implies,  is  a  widely- 
extended,  continuous  layer  or  sheet  of  cloud,  increasing  from 
below  upwards.     It  is,  besides,  the  lowest  sort  of  cloud,   its 
lower  surface  commonly  resting  on  the  earth.     The  stratus  may 
be  called  the  cloud  of  night,  since  it  generally  forms  about  sun- 


APPENDIX. 


341 


H 


CLOUDS. 


342  APPENDIX. 

set,  grows  denser  during  the  night,  and  disappears  about  sun- 
rise. It  is  caused  by  the  vapors  which  rise  during  the  day,  but 
towards  evening  fall  to  the  earth  with  the  falling  temperature. 
Since  during  night  the  cooling  of  the  air  begins  on  the  ground, 
the  stratus  first  appears  like  a  thin  mist  floating  near  the  surface 
of  the  earth  ;  it  thence  increases  upwards  as  successive  layers 
of  the  air  are  cooled  below  the  point  of  saturation.  It  includes 
all  those  mists  already  described,  which  in  the  calm  evening  of 
a  warm  summer  day  form  in  the  bottom  of  valleys  and  over  low- 
lying  grounds,  and  then  spread  upwards  over  the  surrounding 
country  like  an  inundation. 

When  the  morning  sun  shines  on  the  upper  surface  of  the 
stratus  cloud,  it  begins  to  be  agitated  and  to  heave  up  in  dif- 
ferent places  into  the  rounded  forms  of  the  cumulus,  and  the 
whole  of  its  lower  surface  begins  to  rise  from  the  ground.  As 
the  heat  increases,  it  continues  to  ascend,  breaks  up  into  de- 
tached masses,  and  soon  disappears.  This  indicates  a  continu- 
ance of  fine  weather. 

31.  Cirro-cumulus.  —  This  cloud  is  composed  of  well-defined, 
small,  roundish  masses,  lying  near  each  other,  and  quite  sepa- 
rated by  intervals  of  sky.     It  is  formed  from  the  cirrus  cloud, 
the  fibres  of  which  break,  and  gather  into  these  small  masses. 
It  is  commonly  known  among  sailors  as  a  mackerel  sky. 

32.  Cirro-stratus.  —  The  cirro-stratus  partakes  partly  of  the 
characteristics  of  the  cirrus  and  stratus.     It  consists  of  long, 
thin,  horizontal  clouds,  with  bent 'or  undulated  edges,  and  either 
separate  or  in  groups.     It  is  a  marked  precursor  of  storms. 

33.  Cumulo-stratus.  —  T\i\*  cloud  is  formed  by  the  blending 
of  the  cirro-stratus  with  the  cumulus,  either  among  its  piled-up 
heaps,  or  spreading  underneath  its  base  as  a  horizontal  layer. 
It  is  formed  when  the  cumulus  becomes  surrounded  with  small 
fleecy  clouds  just  before  rain  begins  to  fall,  and  also  on  the 
approach  of  thunder-storms. 

34.  Cumulo-cirro- stratus,  or  Nimbus.  —  This  is  the  well-known 
rain-cloud,  consisting  of  a  cloud,  or  system   of  clouds,   from 
which  rain  is  falling.     It  sometimes  has  its  origin  in  the  cumulo- 
stratus,  which  increases  till  it  overspreads  the  sky,  and  becomes 
black  or  bluish-black  in  color  ;  but,  this  soon  changing  to  gray, 
the  nimbus  is  formed,  and  rain  begins  to  fall. 


APPENDIX.  343 

Its  name,  cumulo-cirro-stratus,  suggests  the  way  in  which  it 
is  usually  formed.  At  a  considerable  height,  a  sheet  of  cirro- 
stratus  cloud  is  spread  out,  under  which  cumulus  clouds  drift 
from  the  windward  ;  these  rapidly  increase  and  unite  into  a 
continuous  gray  mass,  from  which  the  rain  falls.  The  breaking 
up  of  this  gray  mass  indicates  that  the  rain  will  soon  cease. 

When  a  rain-cloud  is  seen  approaching  at  a  distance,  cirri 
appear  to  shoot  out  from  its  top  in  all  directions  ;  and  the  more 
copious  the  rain-fall,  the  greater  is  the  number  of  these  cirri. 

RAIN,  SNOW,  AND  HAIL. 

35.  Rain.  — Whatever  lowers  the  temperature  of  the  air  may 
be  considered  as  a  cause  of  rain.  It  is  chiefly  brought  about 
by  the  ascent  of  air  into  the  higher  regions  of  the  atmosphere. 
Moist  air-currents  are  forced  up  into  the  higher  parts  of  the 
atmosphere  by  colder,  drier,  and  therefore  heavier,  wind-cur- 
rents which  get  beneath  them.  Ranges  of  mountains  also 
oppose  their  masses  to  the  winds,  so  that  the  air  forced  up 
their  slopes  is  cooled,  and  its  vapor  condensed  into  showers 
of  rain  or  snow.  Moist  air-currents  are  also  drawn  up  into  the 
higher  regions  of  the  atmosphere  over  the  area  of  least  pressure 
at  the  centre  of  storms  ;  and  in  such  cases  the  rain-fall  is  gen- 
erally very  heavy.  The  temperature  of  the  air  is  lowered,  and 
the  amount  of  the  rain-fall  increased,  by  those  winds  which 
convey  the  air  to  higher  latitudes.  This  occurs  in  temperate 
regions,  or  in  those  tracts  traversed  by  the  return  trade-winds, 
which  in  the  north  temperate  zone  blow  from  the  southwest, 
and  in  the  south  temperate  zone  from  the  northwest.  The 
meeting  and  mixing  of  winds  of  different  temperatures  is  also 
a  cause  of  rain,  since  the  several  portions,  when  combined  into 
one,  cannot  hold  as  much  vapor  as  before.  The  rain-fall  is  also 
increased  if  the  prevailing  winds  are  directly  from  the  sea,  and 
are  therefore  moist;  but  it  is  diminished  if  they  have  passed 
over  large  tracts  of  land,  particularly  mountain-ranges,  and  are 
therefore  dry.  The  quantity  of  rain  is  influenced  by  sandy 
deserts,  which  allow  radiation,  by  day  or  night,  to  take  im- 
mediate effect  in  raising  or  depressing  the  temperature  ;  and 
also  by  forests,  which  retard  or  counteract  radiation. 


344  APPENDIX. 

Rain  rarely  or  never  falls  in  certain  places,  which  are,  on  that 
account,  called  rainless  regions ;  as,  for  example,  the  coast 
of  Peru,  in  South  America,  the  Sahara  in  Africa,  and  the  desert 
of  Gobi,  in  Asia. 

The  Sahara  is  bounded  on  the  north  and  on  the  south  by 
ranges  of  mountains.  When  the  northeast  trade-wind  strikes 
the  northern  range,  a  part  of  its  vapor  is  condensed.  As  it 
moves  southward,  it  reaches  warmer  latitudes,  where  there  is 
a  greater  capacity  for  moisture.  Since  there  are  no  opposing 
winds  to  force  it  upwards,  it  sweeps  on  across  the  vast  sandy 
plain  until  it  arrives  at  the  southern  mountains,  where  its  vapor 
is  precipitated  in  abundant  rains.  In  the  few  spots  in  the 
desert  where  hills  or  mountains  occur,  there  are  occasional 
rains. 

On  the  desert  of  Gobi,  the  prevailing  winds  are  from  the 
southeast,  and  are  very  dry,  because  they  have  precipitated 
nearly  all  their  moisture  in  passing  over  the  Himalaya  Moun- 
tains. 

The  rainless  district  in  Peru  is  caused  by  the  Andes,  which 
condense  nearly  all  the  vapor  of  the  southeast  trade-wind  in 
copious  rains  on  their  eastern  slopes. 

On  the  other  hand,  in  such  places  as  Chili  and  Patagonia,  it 
rains  almost  every  day. 

36.  Rain-fall  within  the  Tropics.  —  At  places  within  the 
tropics,  where  the  trade-winds  blow  regularly  and  steadily,  the 
rain-fall  is  small.  Since  these  winds  come  from  higher  lati- 
tudes, the  temperature  is  increasing,  and  they  are  thus  more 
likely  to  take  up  moisture  than  to  paft  with  it.  Where,  how- 
ever, the  trade-winds  are  forced  up  the  slopes  of  mountain 
ranges,  they  bring  rain  in  copious  showers. 

The  tropical  belt,  known  as  the  region  of  calms  (see  page  326) 
is  the  region  of  constant  rains.  Here  the  sun  almost  invariably 
rises  in  a  clear  sky ;  but  about  midday  clouds  gather,  and  the 
whole  face  of  the  sky  is  soon  covered  with  black  clouds,  which 
pour  down  prodigious  quantities  of  rain.  Towards  evening  the 
clouds  disappear,  the  sun  sets  in  a  clear  sky,  and  the  nights 
are  serene  and  fine.  The  reason  of  this  is,  that  the  air,  being 
greatly  heated  by  the  vertical  rays  of  the  sun,  ascends,  drawing 
with  it  all  the  vapor  which  the  trade-winds  have  brought  with 


APPENDIX.  345 

them,  and  which  has  been  largely  increased  by  the  rapid  evap- 
oration from  the  belt  of  calms  ;  and  this  vapor  is  condensed  as 
it  rises.  The  rain  is  sometimes  so  copious  that  fresh  water 
has  been  collected  from  the  surface  of  the  sea.  As  evening 
sets  in,  the  surface  of  the  earth  and  the  air  near  it  being  cooled, 
the  ascending  currents  cease,  and  the  cooled  air  descends  ;  the 
clouds  are  thus  dissolved,  and  the  sky  continues  clear  till  the 
returning  heat  of  the  following  day. 

Over  a  great  part  of  the  tropics  disturbing  influences  draw 
the  trade-winds  out  of  their  course,  and  sometimes,  as  in  the 
case  of  the  monsoons,  give  rise  to  winds  which  blow  from  the 
opposite  point  of  the  compass.  These  winds  affect  the  rain-fall 
of  India,  and  but  for  them  the  eastern  districts  of  Hindostan 
would  be  constantly  deluged  with  rain,  and  the  western  districts 
constantly  dry  and  arid.  As  it  is,  each  part  of  India  has  its 
dry  and  wet  seasons,  summer  being  the  wet  season  of  the  west 
and  interior  as  far  as  the  Himalaya,  and  winter  the  wet  season 
of  the  east,  and  especially  the  southeast. 

So  far  as  known,  the  heaviest  annual  rain-fall  at  any  place 
on  the  globe  is  600  inches  on  the  Khasia  Hills.  About  500 
inches  of  this  fall  in  seven  months,  during  the  southwest  mon- 
soons. These  hills  face  the  Bay  of  Bengal,  from  which  they 
are  separated  by  only  200  miles  of  swamps  and  marshes. 
Hence  the  southerly  winds  not  only  arrive  heavily  laden  with 
vapor  from  the  Indian  Ocean,  but  they  get  more  moisture  in 
passing  over  the  200  miles  of  swamp.  They  are,  therefore, 
ready  to  burst  in  torrents,  even  before  they  are  suddenly  raised, 
by  the  hills  they  encounter,  into  the  cooler  regions  of  the  atmos- 
phere. 

37.  Snow.  —  Snow  is  the  frozen  moisture  which  falls  from 
the  clouds  when  the  temperature  is  32°  or  lower.  The  particles 
of  which  snow  is  composed  are  crystals,  which  are  usually  in 
the  form  of  six-pointed  stars.  About  1,000  different  kinds  of 
snow-crystals  have  been  already  observed,  a  few  of  which  are 
shown  in  Figure  229.  The  forms  of  the  crystals  of  the  same 
fall  of  snow  are  generally  similar  to  each  other.  Snow-flakes 
vary  from  an  inch  to  .07  of  an  inch  in  diameter,  the  largest 
being  observed  when  the  temperature  is  near  32°,  and  the 
smallest  at  very  low  temperatures. 
15* 


346  APPENDIX. 

The  limit  of  the  fall  of  snow  at  any  time  of  the  year  coincides 
nearly  with  30°  N.  latitude,  which  includes  almost  the  whole  of 
Europe.  On  traversing  the  Atlantic,  this  line  rises  to  45°,  but 
on  nearing  the  American  continent  it  descends  to  33°  ;  it  rises 
in  the  west  of  America  to  47°,  and  again  falls  to  40°  in  the 
Pacific.  Snow  is  unknown  at  Gibraltar;  at  Paris,  it  falls  12 
days  on  an  average  annually,  and,  at  St.  Petersburg,  170  days. 

The  white  color  of  snow  is  caused  by  the  combining  of  the 
different  prismatic  rays  which  issue  from  the  minute  snow- 
crystals.  When  the  crystals  are  looked  at  separately,  some 

Fig.  229. 


appear  red,  others  green,  purple,  and,  in  short,  all  the  colors  of 
the  spectrum  ;  but  when  a  mass  of  snow  is  looked  at,  the 
different  colors  blend  into  white. 

Red  snow  and  green  snow  have  been  occasionally  met  with  in 
the  arctic  regions  and  in  other  parts  of  the  world.  These 
colors  are  due  to  the  presence  of  vegetable  organisms,  about 
.001  of  an  inch  in  diameter,  which  grow  and  flourish  in  the 
region  of  eternal  snow. 

From  its  loose  texture,  and  from  its  containing  about  ten 
times  its  bulk  of  air,  snow  is  a  very  bad  conductor  of  heat ;  and 
thus  is  an  admirable  covering  to  preserve  the  earth  from  the 
effects  of  its  own  radiation.  It  not  unfrequently  happens  in 
times  of  great  cold,  that  the  soil  is  40°  warmer  than  the  surface 
of  the  snow  which  covers  it.  The  flooding  of  rivers,  from  the 
melting  of  the  snow  on  mountains  in  spring  and  summer, 
carries  fertility  into  regions  which  would  otherwise  remain 
barren  wastes. 

38.  Hail.  —  Hailstones  are  generally  of  a  conical  or  of  a 
round  shape,  and,  when  cut  across,  are  found  to  be  composed 
of  alternate  layers  of  clear  and  opaque  ice,  enveloping  a  white 
snowy  nucleus.  Less  frequently  they  are  composed  of  crystals 


APPENDIX.  347 

radiating  from  the  centre  outwards.  They  vary  much  in  size, 
some  being  as  small  as  the  smallest  shot,  while  others  are  several 
inches  in  diameter.  In  August,  1813,  hailstones  the  size  of 
eggs  fell  upon  the  British  army  among  the  Pyrenees  ;  the 
storm  lasted  twenty  minutes,  and  was  not  accompanied  with 
thunder  or  lightning.  June  4th,  1814,  hail,  from  13  to  15  inches 
in  diameter,  fell  in  Ohio.  In  the  Orkney  Islands,  July  24th, 
1818,  during  thunder,  a  very  remarkable  shower  of  hail  took 
place  ;  the  stones  were  as  large  as  a  goose's  egg,  and  mixed 
with  large  masses  of  ice. 

The  origin  of  hail  is  not  fully  understood  ;  but  it  appears  to 
be  formed  by  a  cold  current  of  air  forcing  its  way  into  a  mass 
of  air  much  warmer  and  nearly  saturated,  the  temperature  ot 
the  united  mass  being  below  the  freezing-point.  The  warm, 
moist  air  is  easily  accounted  for,  since  hail  generally  falls  in 
summer  and  during  the  day  ;  but  it  is  difficult  to  account  for  the 
intensely  cold  current  which  is  sufficient  to  reduce  the  warm 
saturated  mass  below  32°. 

In  mountainous  regions,  cold  currents  from  the  fields  of 
snow,  rushing  down  the  sides  of  the  mountains  and  mixing  with 
the  heated  air  of  the  valleys,  are  no  doubt  frequent  causes  of 
hail ;  and  such  places  are  peculiarly  subject  to  hailstorms. 

The  sudden  ascent  of  moist  warm  air  into  the  upper  regions 
of  the  atmosphere,  where  a  cold  current  prevails  at  the  time,  is, 
in  all  probability,  a  common  cause  of  hail.  This  is  confirmed 
by  the  sultry,  close  weather  which  generally  precedes  hail- 
storms, the  slight  but  sudden  fall  of  the  barometer,  the  whirl- 
winds and  ascending  currents  which  accompany  them,  and  the 
fall  in  the  temperature  which  follows  after  the  storm  has  passed. 

ATMOSPHERIC    ELECTRICITY. 

39.  Electricity  in  the  Air. — The  identity  of  lightning  and 
electricity  was  first  suspected  by  Wall  in  1708,  but  it  was  re- 
served to  Franklin  to  prove  it.  In  1749,  he  suggested,  as  the 
mode  of  proof,  the  erection  of  pointed  metallic  conductors  prop- 
erly insulated.  Acting  on  this  suggestion,  Dalibard  erected 
near  Paris  a  pointed  iron  rod,  40  feet  in  length,  and  insulated  ; 
and,  on  the  loth  of  May,  1752,  obtained  electrical  sparks  from 


348  APPENDIX. 

it.  In  June  of  the  same  year,  Franklin,  impatient  at  the  delay 
in  erecting  the  spire  for  his  pointed  conductor,  tried  the  experi- 
ment of  obtaining  electricity  from  the  clouds  by  flying  a  kite. 
The  kite  was  held  by  a  hempen  string,  to  the  lower  end  of 
which  a  key  was  attached ;  and  the  whole  was  insulated  by 
tying  a  silk  ribbon  to  the  key,  the  other  end  of  the  ribbon 
being  attached  to  a  post.  On  the  approach  of  the  thunder- 
cloud, he  raised  the  kite,  and  soon  the  fibres  of  the  hempen 
string  began  to  repel  each  other ;  and,  at  last,  when  the  rain 
had  moistened  the  string,  he  had  the  satisfaction  of  drawing 
sparks  from  the  key. 

When  the  sky  is  cloudless,  the  electricity  is  always  positive; 
but  the  intensity  increases  with  the  height. 

When  the  sky  is  clouded,  the  electricity  is  sometimes  positive 
and  sometimes  negative,  according  to  the  electrified  condition  of 
the  clouds.  In  relation  to  the  air,  the  earth's  surface  is  always 
negative. 

The  electricity  of  the  atmosphere  is  stronger  in  winter  than 
in  summer,  increasing  from  June  to  January,  and  decreasing 
from  January  to  June.  It  is  subject  to  a  double  maximum  and 
minimum  each  day.  . 

40.  Sources  of  Atmospheric  Electricity.—  (i)  Evaporation.  — 
Electricity  is  produced  when  impure  water  is  evaporating,  or 
water  in  which  chemical  decomposition  is  going  on  ;  none 
whatever  being  produced  by  the  evaporation  of  pure  water. 
Evaporation  from  water  containing  an  alkali  or  a  salt  gives 
off  negative  electricity  to  the  air,  and  leaves  positive  electricity 
behind  ;  but  when  the  water  contains  acid,  positive  electricity  is 
given  off,  and  negative  is  left  behind.  Hence  it  is  supposed 
that  seas,  lakes,  and  rivers  are  abundant  sources  of  electricity, 
particularly  of  the  positive  sort.  (2)  Vegetation.  —  The  vege- 
table kingdom  is  also  a  source  of  electricity  ;  (a)  from  the  evap- 
oration going  on  by  which  water  is  separated  from  the  sap  of 
the  plants,  and  (b)  from  the  giving  off  of  oxygen  gas  during 
the  day,  and  carbonic  gas  during  the  night.  In  these  cases, 
positive  electricity  arises  from  the  plants,  and  negative  is  left 
behind.  (3)  Combustion.  —  During  the  process  of  burning, 
bodies  give  off  positive  electricity,  and  become  themselves  neg- 
atively electrified.  This  is  frequently  seen  on  a  grand  scale 


APPENDIX.  349 

during  volcanic  eruptions.  (4)  Friction.  —  Wind,  by  the  fric- 
tion it  produces  upon  terrestrial  objects,  the  particles  of  dust, 
and  the  watery  particles  which  it  carries  with  it,  contributes  to 
the  electricity  of  the  air.  Electricity  is  not  generated  if  the 
moisture  be  in  the  form  of  pure  vapor. 

41.  Effect  of  the  Condensation  of  Vapor.  — When  a  great  mul- 
titude of  molecules  of  vapor  are  condensed  by  cold  into  a  drop, 
or  snow-spangle,  that  drop  probably  collects  and  retains  on  its 
surface  the  whole  electricity  of  the  molecules  from  which  it  is 
formed.     If  a  thousand  such  globules  coalesce  into  one,  the 
electricity  will  be  increased  a  thousand-fold,  and,  being  spread 
entirely  over  the  surface,  will  have  a  tenfold  tension.     This 
view  (which   is   Sir  John    Herschel's)  explains  the  electricity 
observed  in  the  lower  stratum  of  air  when  dew  is  being  de- 
posited,  and  the   highly  electrical   state   of  fogs  and  clouds. 
It  also  explains  the  annual  fluctuation  ;    for,   since  in  winter 
the  condensation  of  vapor  is  greater  and  more  frequent  than 
in  summer,  the  average  quantity  of  electricity  will  be  greater 
in  winter. 

42.  Thunder-storms.  —  The  thunder-storm  probably  originates, 
like  cloud  and  rain,  in  the  condensation  of  vapor  ;  but  the  con- 
densation is  more  copious  and  more  rapid,  so  as  to  bring  about 
an  accumulation   of  a  sufficient  quantity  of  electricity.     If  the 
condensation  is  not  copious,  the  electricity  will  be  too  weak  ; 
and  if  not  sudden,  it  escapes  before  enough  collects  for  a  dis- 
charge. 

Thunder-storms  occur  most  frequently  within  the  tropics, 
and  diminish  in  frequency  towards  the  poles.  They  are  also 
more  frequent  in  summer  than  in  winter  ;  during  day  than 
during  night ;  after  midday  than  before  it  ;  and  in  mountainous 
countries  than  in  plains.  Within  the  tropics  they  prevail  most 
in  the  region  of  calms  and  during  the  rainy  season  ;  and  least 
in  arid  deserts  and  during  the  dry  season. 

43.  Lightning.  —  Arago  has  divided  lightning  into  three 
kinds ;  zigzag  lightning,  sheet  lightning,  and  ball  lightning. 
When  the  electric  flash  darts  through  the  air,  it  takes  the  path 
of  least  resistance;  and,  since  the  conducting  power  of  different 
portions  of  the  atmosphere  is  unequal,  the  lightning  frequently 
appears  zigzag.  When  branches  are  given  off  at  different 


350  APPENDIX. 

points  of  its  course,  the  lightning  is  said  to  be  forked.  Sheet- 
lightning  is  the  most  common,  appearing  as  a  glow  of  light 
illuminating  the  sky.  The  flashes  often  follow  each  other  in 
quick  succession,  and  the  thunder  which  accompanies  them  is 
low  and  at  a  considerable  distance.  Analogous  to  this  is  silent 
lightning,  frequently  termed  heal  lightning,  which  generally 
occurs  during  serene  summer  evenings,  lighting  up  the  sky  fit- 
fully for  hours,  with  repeated  faint  flashes  ;  it  is  not  attended 
with  thunder.  It  is  probable  that  this  kind  of  lightning  is  al- 
most always  the  reflection  of  the  lightning  of  distant  storms 
from  the  vapor  of  the  upper  regions  of  the  atmosphere,  the 
storms  themselves  being  so  far  off  that  their  thunder  cannot  be 
heard.  Ball  lightning  is  the  least  common.  It  appears  as  a 
globular  mass,  moving  slowly  or  sometimes  remaining  station- 
ary, and  in  a  short  time  explodes  with  violence.  It  has  not 
yet  been  satisfactorily  explained.  Professor  Wheatstone  has 
shown  that  the  duration  of  a  flash  of  lightning  is  less  than  the 
thousandth  part  of  a  second.  A  wheel  was  made  to  rotate  so 
rapidly  that  the  spokes  were  invisible  ;  on  being  lighted  up 
with  the  electric  flash,  the  duration  of  the  flash  was  so  brief 
that  the  wheel  appeared  quite  stationary,  even  though  rotating 
with  the  utmost  speed  possible. 

44.  Thunder.  —  Thunder  is  probably  the  noise  produced  by 
the  instantaneous  rushing  of  the  air  to  fill  the  vacuum  left  by 
the  lightning  along  the  path  of  the  discharge.  The  sound 
emitted  by  flames  is  a  familiar  illustration  of  a  similar  phenom- 
enon. Flashes  of  lightning  frequently  extend  two  or  three 
miles  in  length  ;  and  since  the  thunder  is  produced  at  every 
point  along  its  course  nearly  at  the  same  instant,  the  prolonged 
rolling  noise  of  thunder  arises  from  the  different  intervals  of  time 
it  takes  the  sound  to  reach  the  ear.  For  since  sound  travels  at 
the  rate  of  1,090  feet  per  second,  it  is  first  heard  from  the  near- 
est point  of  the  flash,  later  and  later  from  points  more  distant, 
so  that  the  combined  effect  is  a  continued  peal  of  thunder.  The 
direction  and  character  of  the  peal  will  depend  on  the  length  of 
the  flash,  and  the  greater  or  less  obliquity  of  its  course  in  rela- 
tion to  the  observer.  Reverberations  from  clouds  and  from 
mountains  frequently  heighten  the  effect  and  prolong  the  peal. 
From  the  rate  at  which  sound  travels,  if  the  thunder  is  not 


APPENDIX.  351 

heard  till  five  seconds  after  the  flash,  the  distance  is  about  a 
mile.  Thunder  has  not  been  heard  at  a  greater  distance  than 
14  miles  from  the  flash. 

45.  Effects  of  Lightning.  —  The  great  proportion  of  electrical 
discharges  pass  into  the  air,  or   into  other  clouds  less  highly 
electrified  ;  a  very  few  only  take  place  between  the  cloud  and 
the  earth.     The  destructive  effects  of  this  latter  class  are  known 
to  all.     By  the  electric  discharge  innumerable  lives  have  been 
destroyed,  the  strongest  trees  rent  to  pieces,  heavy  bodies  dis- 
placed, iron  and  steel  magnetized,  metals  and  rocks  softened 
and  fused,  and  combustible  substances  set  on  fire.     When  the 
thunderbolt  falls  upon  sand  it  usually  produces  fulgurites  or 
fulminary  tubes,  which  are  silicious  tubes  of  various  sizes  vitri- 
fied internally. 

46.  Return  Shock.  —  This  shock  sometimes  proves  fatal  to 
living  beings,  even  at  great  distances  from  the  place  where  the 
electric  discharge  takes  place.     It  is  caused  by  the  inductive 
action  of  the  electrified  cloud  on  bodies  within  the  sphere  of  its 
influence,  by  which  they  become  charged  with  the  electricity 
opposite  to  that  of  the  cloud.     Hence,  when  the  cloud  has  dis- 
charged its  electricity  into  the  ground,  the  induction  ceases  and 
a  rapid  change  takes  place  in  bodies  from  the  electrified  to  the 
neutral  state,  thus  causing  the  concussion  of  the  return  shock. 

47.  Lightning- Rods.  —  The  lightning-rod  was  introduced  by 
Franklin  in  1755  as  a  means  of  protecting  buildings  from  the 
destructive  effects  of  electricity.     The  advantage  gained  by  it 
consists  not  in  protecting  the  building  in  case  of  a  discharge 
by  allowing  a  free  passage  for  the  electric  fluid  to  escape  to  the 
earth,  for  it  is  but  a  poor  protection  in  such  a  case  ;  but,  by 
quietly  and  gradually  keeping  up  the  communication,  it  tends 
to  maintain  the  electric  equilibrium,  and  thus  prevent  the  oc- 
currence of  a  discharge.    The  best  rods  are  made  of  copper  not 
less  than  three  quarters  of  an  inch  thick,  and  pointed  at  the 
upper  end.     They  should  be  of  one  piece  throughout,  fastened 
vertically  to  the  roof  of  the  building,  and  thence  carried  down 
into  the  ground.     The  lower  extremity  should  part  into  two  or 
three  branches  bent  away  from   the   house,  and  carried  suffi- 
ciently far  into  the  soil  to  meet  water  or  permanently  moist 
earth.     The  conductor  should  be  connected  with  all  metallic 


352  APPENDIX. 

surfaces  on  the  roof  or  other  parts  of  the  building,  in  order  to 
prevent  the  occurrence  of  lateral  discharges,  or  discharges  from 
the  conductor  to  these  surfaces,  which  are  often  very  destruc- 
tive. 

48.  St.  Elmo's  Fire.  —  This  meteor  is  the  Castor  and  Pollux 
of  the  ancients,  and  is  frequently  mentioned  in  classic  writings, 
from  the  Argonautic  expedition  downwards.     Caesar  notices  its 
appearance  after  a  storm  of  hail  in  these  words  :  "  Eadem  nocte 
legionis  quintae  cacumina  sua  sponte   arserunt."     The  finest 
and  most  beautiful  displays  occur  at  sea  during  storms,  when 
it  appears  as  a  light  resting  on  the  masts.     The  light  which 
is  seen  on  a  point  held  near  the  conductor  of  an  electric  ma- 
chine explains  St.  Elmo's  fire,  which  takes  place  when  the  elec- 
tricity of  a  cloud  and  that  of  the  earth  combine,  not  in  flashes 
of  lightning,  but  slowly  and  continuously  from  different  points. 

49.  The  Aurora  Borealis. —  The  aurora  borealis  is  the  lumi- 
nous appearance  in  the  northern  sky,  which  forms,  in  its  most 
vivid  displays,  spectacles  of  surpassing  beauty.     The  aurora  is 
observed  also  in  the  neighborhood  of  the  south   pole,  and  is 
there  called  aurora  australis.     When  fully  developed,  the  au- 
rora consists  of  a  dark  segment  of  a  hazy  or  slaty  appearance 
surmounted  by  an  arch  of  light,  from  which  luminous  streamers 
quiver  and   dart  upwards.     Several  auroral  arches  are  some- 
times seen  at  once.     Sometimes  the  streamers  appear  to  unite 
near  the  zenith,  forming  what  is  called  the  corona  of  the  aurora, 
towards  which  the  dipping  needle  at  the  time  points. 

Auroras  are  very  unequally  distributed  over  the  earth's  sur- 
face. At  Havana  but  six  have  been  recorded  within  a  hundred 
years.  As  we  travel  northwards  from  Cuba,  they  increase  in 
frequency  and  brilliancy  ;  they  rise  higher  in  the  heavens,  and 
oftener  attain  the  zenith.  If  we  travel  northwards  along  the 
meridian  of  Washington,  we  find  on  an  average  near  the  par- 
allel of  40°  only  ten  auroras  annually.  Near  the  parallel  of 
42°,  the  average  number  is  twenty  annually ;  near  45°,  it  is 
forty  ;  and  near  50°,  it  is  eighty.  Between  this  point  and  the 
parallel  of  62°  auroras  are  seen  almost  every  night,  high  in  the 
heavens,  and  as  often  to  the  south  as  the  north.  Farther  north 
they  are  seldom  seen  except  in  the  south,  and  from  this  point 
they  diminish  in  frequency  and  brilliancy  as  we  advance  towards 


APPENDIX.  353 

the  pole.  If  we  make  a  like  comparison  for  the  meridian  of  St. 
Petersburg,  we  shall  find  a  similar  result,  except  that  the  auroral 
region  is  situated  farther  northward  than  it  is  in  America.  Au- 
roras are  more  frequent  in  the  United  States  than  they  are  in 
the  same  latitudes  of  Europe. 

The  aurora  is  of  great  extent,  having  been  sometimes  ob- 
served simultaneously  in  Europe  and  America.  From  obser- 
vations made  in  the  two  hemispheres,  Professor  Loomis  thinks 
it  probable  that  an  exhibition  of  auroral  light  about  one  mag- 
netic pole  of  the  earth  is  uniformly  attended  by  a  simultaneous 
exhibition  of  auroral  light  about  the  opposite  magnetic  pole.* 
The  height  varies  from  about  45  to  500  miles  above  the  earth. 

50.  Relations  of  the   A^trora   to   Magnetism. —  Many   facts 
point  out  an  evident  connection  between  the  aurora  and  terres- 
trial magnetism.     The  magnetic  needle  is  much  agitated  when 
the  aurora  is  visible.     When  the  arch  is  motionless,  so  is  the 
needle  ;  but  as  soon  as  streamers  are  shot  out,  its  declination 
changes  every  moment,  and  this  happens  though  the  aurora 
does  not  appear  at  the  place  of  observation,  but  is  seen  near  the 
pole.    Captain  M'Clintock,  when  in  the  arctic  regions,  observed 
that  the  aurora  in  all  cases  appeared  to  come  from  the  surface 
of  open  water,  and  not  in  any  case  from  the  fields  of  ice.     This 
favors  the  idea  that  it  is  caused  by  electrical  discharges  between 
the  earth  and  the  air,  and  that  these  are  interrupted  by  the 
fields  of  non-conducting  ice. 

General  Sabine  has  discovered  that  magnetic  disturbances  of 
the  earth  are  due  to  the  sun,  but  not  to  his  heat  and  light ;  and 
are  invariably  accompanied  by  the  aurora  and  by  electric  cur- 
rents on  the  surface  of  the  earth.  The  secular  periods  of  the 
sun's  spots,  of  the  variation  of  the  magnetic  needle,  and  of  the 
frequency  of  auroras,  coincide  in  a  remarkable  way,  indicating 
that  these  phenomena  are  regulated  by  astronomical  causes.f 

OPTICAL  PHENOMENA. 

51.  The  Rainbow.  —  For  the  description  and  explanation  of 
the  rainbow,  see  pages  144-  147. 

*  Treatise  on  Meteorology,  p.  188.  t  See  Handbook  of  the  Stars,  p.  91. 


354  APPENDIX. 

Since  rainbows  in  the  morning  are  always  seen  in  the  west, 
they  indicate  the  advance  of  the  rain-cloud  from  the  west  at  the 
lime  that  it  is  clear  and  bright  in  the  east  ;  and  since  the  fall  of 
rain  at  this  time  of  the  day  when  the  temperature  should  be  ris- 
ing is  an  additional  evidence  of  increasing  moisture,  a  morning 
rainbow  is  regarded  as  a  prognostic  of  a  change  to  wet,  stormy 
weather.  On  the  contrary,  the  conditions  under  which  a  rain- 
bow can  appear  in  the  evening  are,  the  passing  of  the  rain-cloud 
to  the  east,  and  a  clearing  up  in  the  west  at  the  time  of  day 
when  the  temperature  has  begun  to  fall,  thus  further  indicat- 
ing a  change  from  wet  to  dry  weather.  Hence  the  popular 
rhyme :  — 

"  A  rainbow  in  the  morning,  — 
Sailors  take  warning ; 
A  rainbow  at  night 
Is  the  sailor's  delight." 

52.  Lunar  Rainbows.  —  Rainbows  are  also  produced  by  the 
light  of  the  moon  falling  on  rain-drops,  exactly  in  the  same  way 
as  solar  rainbows.     They  are  by  no  means  of  rare  occurrence. 
Owing  to  the  feeble  light  of  the  moon  the  bow  is  generally  with- 
out colors  ;  but  when  the  sky  is  very  clear  and  the  moon  at  the 
full,  the  prismatic  colors  appear,  but  in  subdued  splendor. 

53.  Coronas.  —  The  corona  is  an  appearance  of  faintly-colored 
rings  encircling  the  moon  when  seen  behind  the  light,  fleecy 
cloud  of  the  cirro-cumulus.     When  the  corona  is  perfect,  the 
rings  form  several  concentric  circles,  the  blue  prism-itic  color 
being  nearer  the  centre  than  the  red.     When  of  large  dimen- 
sions the  ring  has  generally  a  whitish,  nebulous  appearance. 

Coronas  are  also  very  frequently  formed  round  the  sun  ;  but 
to  see  them  it  is  necessary  to  look  through  smoked  glass,  or  at 
the  image  of  the  sun  reflected  from  still  water. 

54.  Anthelia.  —  Glories  of  light,  otherwise  called  anthelia, 
because  formed  opposite  the  sun,  are  sometimes  seen  when  the 
shadow  of  an  observer  is  cast  on  fog  ;  and  the  shadow  of  his 
head  is  surrounded  with  the  prismatic  circles.     On  one  occa- 
sion Scoresby  saw  four  colored  concentric  circles  around  his 
shadow,   and   he  observed  that   the  phenomenon  was  always 
seen  in  the  polar  regions  whenever  sunshine  and  fog  occurred 
at  the  same  time. 


APPENDIX. 


355 


55.  Halos.  —  Halos  are  circles  of  prismatic  colors  around  the 
sun  (Figures    230-233)  or  the  moon  (Figures   234  and  235). 


Fig.  230. 


Fig.  231. 


Fig.  232. 


Fig-  233. 


Fig.  235- 


but  they  are  perfectly  distinct  from  coronas,  with  which  they 
should  not  be  confounded.     Halos   are  of  comparatively  rare 


356  APPENDIX. 

occurrence  ;  coronas,  on  the  contrary,  may  be  seen  every  time 
a  light,  fleecy  cloud  comes  between  us  and  the  sun  or  moon. 
The  structure  of  halos,  as  seen  from  the  figures,  is  often  very 
complicated,  circle  cutting  circle  with  mathematical  exactness, 
the  circles  being  generally  very  large.  The  structure  of  the 
corona,  on  the  other  hand,  is  simple,  the  circles  concentric,  the 
inner  one  small,  the  diameter  of  the  second  being  double,  and 
that  of  the  third  treble,  the  diameter  of  the  first.  In  halos,  the 
red  prismatic  color  is  next  the  centre  ;  in  coronas,  the  blue. 
Halos  are  formed  from  the  refraction  and  reflection  of  the  rays 
of  light  by  the  minute  snow-crystals  of  the  cirrus  cloud  ;  while 
coronas  arise  from  the  interference  of  the  rays  passing  on  each 
side  of  the  globules  of  vapor. 

56.  Parhelia  and  Paraselene.  —  At  the  points  where  the  cir- 
cles of  the  halo  intersect,  images  of  the  sun  or  moon  generally 
appear  from  the  light  concentrated  at  these  points.    The  images 
of  the  sun  are  called  parhelia,  or  mock-suns;  and  those  of  the 
moon,  paraselenes,   or  mock-moons.      These  also   exhibit  the 
prismatic  colors  of  the  halo. 

57.  Colors  of  Clouds.  —  Every  one  has  observed  and  admired 
the  red  and  golden  clouds  which  fire  the  western  sky  at  sunset, 
and  make  "  the  day's  dying  glory."     They  are  observed  to  be 
the  accompaniment  of  cumulus  clouds  as  they  slowly  sink,  while 
dissolving,  down  into  the  lower  and  warmer  parts  of  the  atmos- 
phere ;  and  consequently  they  disappear  from  the  sky  shortly 
after  sunset.     Such  sunsets  are  therefore  universally  regarded 
as  prophetic  of  fine  weather. 

A  green  or  yellowish-green  tinted  sky,  on  the  other  hand,  is 
one  of  the  surest  prognostics  of  rain  in  summer,  and  snow  in 
winter.  The  changing  tints  of  the  evening  sky  after  stormy 
weather  supply  valuable  help  in  forecasting  the  weather  ;  for,  if 
the  yellow  tint  becomes  of  a  sickly  green,  more  rain  and  stormy 
weather  may  be  expected  ;  but  if  it  deepens  into  orange  and  red, 
the  atmosphere  is  getting  drier,  and  fine  weather  may  be  looked 
for. 

Some  years  ago,  Forbes  showed  from  experiments  that  high- 
pressure  steam,  while  transparent,  and  in  the  act  of  expansion, 
readily  absorbs  the  violet,  blue,  and  part  of  the  green  rays,  thus 
letting  the  yellow,  orange,  and  red  pass.  Dr.  E.  Lommel  has 


APPENDIX.  357 

shown  that  successive  layers  of  air  with  visible  vapor  diffused 
through  them  act,  so  to  speak,  like  sieves,  which  continually 
separate  the  transmitted  light  more  and  more  perfectly  from  its 
more  refrangible  rays.  Hence,  in  passing  through  different 
thicknesses  of  vapor,  the  blue  rays  are  first  absorbed,  then  the 
yellow  rays,  and  finally  the  red  rays.  It  is  in  the  lower  layers 
of  the  atmosphere  that  dust,  smoke,  watery  vapor,  and  small 
rain-drops  are  chiefly  suspended.  When  the  sun  is  high  in  the 
heavens,  the  thickness  of  the  vapor-screen  between  the  sun  and 
the  eye  is  not  sufficient  to  produce  any  perceptible  action  on 
the  rays  of  light,  which  consequently  appear  white  ;  but  as  the 
sun  descends  to  the  horizon  the  thickness  of  the  vapor  is 
greatly  increased,  and  at  sunset  it  is  calculated  that  the  light 
of  the  sun  has  to  pass  through  200  miles  of  the  air  in  illuminat- 
ing a  cloud  a  mile  above  the  earth.  Hence,  as  the  rays  fall 
more  and  more  obliquely  on  the  clouds,  they  appear  succes- 
sively yellow,  orange,  and  finally  red.  The  varied  colors  often 
seen  at  sunset  are  due  to  the  fact  that  the  clouds  appear  at  dif- 
ferent heights  and  in  different  parts  of  the  sky,  so  that  various 
thicknesses  of  vapor  are  interposed  between  them  and  the  sun. 
At  dawn  the  clouds  first  appear  red  ;  but,  as  the  sun  rises  high- 
er, the  yellow  light  ceases  to  be  absorbed,  and  they  appear 
orange,  yellow,  and  finally  white.  These  successive  stages  of  a 
perfect  dawn  are  well  described  in  Dante's  Purgatorio  :  — 

"  The  dawn  was  vanquishing  the  matin  hour, 
Which  fled  before  it,  so  that  from  afar 

I  recognized  the  trembling  of  the  sea 

Already  had  the  sun  the  horizon  reached 

So  that  the  white  and  the  vermilion  cheeks 
Of  beautiful  Aurora,  where  I  was, 
By  too  great  age  were  changing  into  orange." 

Longfellow's  translation. 

Milton  has  accurately  described  the  last  stage  of  dawn  in 
U  Allegro:  — 

"  .  .  .  .  the  great  sun  begins  his  state, 
Robed  in  flames  and  amber  light, 
The  clouds  in  thousand  liveries  dight." 

It  is  evident  that  a  high  red  dawn  may  be  regarded  as  a  prog- 
nostic of  settled  weather,  because  the  redness  seen  in  clouds  at 


358  APPENDIX. 

a  great  height  while  the  sun  is  yet  below  the  horizon  may  be 
occasioned  by  the  great  thickness  of  the  vapor-screen  through 
which  the  illuminating  rays  must  pass  before  reaching  the 
clouds,  and  not. to  any  excess  of  vapor  in  the  air  itself.  But  if 
the  clouds  be  red  and  lowering  in  the  morning,  it  may  be  ac- 
cepted as  a  sign  of  rain,  since,  the  thickness  traversed  by  the 
illuminating  rays  being  now  much  less,  the  red  color  must  arise 
from  an  unusual  amount  of  vapor  in  that  stage  of  partial  con- 
densation, when,  according  to  Forbes,  the  blue  rays  are  ab- 
sorbed, and  the  yellow  and  red  pass. 


SOURCES   AND    CONVERSION    OF^ENERGY. 

IgiP"   This  Abridgment  of  the  chapter  in  the  ''''Astronomy'"  on  "Energy"  u 
inserted  for  the  convenience  of  teachers  who  may  not  use  both  books. 

1.  Kinds  of  Energy.  —  Every  moving  body  is  said  to  have  a 
dynamical  energy  ;  and  every  body  which  is  so  situated  that  it 
can  be  moved  by  the  forces  acting  upon  it  is  said  to  have  a  pos- 
sible or  potential  energy.     The  energy  of  a  visible  mass  in  mo- 
tion is  called  mechanical.    The  energy  of  a  moving  molecule  or 
atom  is  called  molecular  or  atomic. 

The  energy  manifested  in  the  bodies  of  animals  is  called  nerve 
force  or  nmscular  energy. 

2.  Affinity,  Cohesion,  and  Gravity  are  the  Forces  which  tend 
to  convert  Potential  into  Dynamical  Energy.  —  When  visible 
masses  are  separated,  gravity  tends  to  pull  them  together,  and 
to  convert  their  potential  into  dynamical  energy.     When  the 
molecules  of  a  body  are  separated  by  melting  and  boiling,  cohe- 
sion tends  to  draw  them  together  again,  and  thus  to  convert 
their  potential  into  dynamical  energy,  which  appears  as  heat. 
Again,  when  the  elements  of  a  compound  are  separated,  chemi- 
cal affinity  tends  to  pull  them  together,  and  to  convert  their 
potential  into  dynamical  energy,  which   appeals,  in   ordinary 
chemical  action,  as  heat  and  electricity,  or,  in  respiration,  as 
heat  and  muscular  force. 

3.  Mechanical  Energy  may  be  converted  inf~*  Heat.  —  We 


APPENDIX.  359 

have  a  familiar  illustration  of  this  in  the  lighting  of  a  friction 
match.  A  portion  of  the  energy  employed  in  rubbing  the 
match  is  converted  by  the  friction  into  heat,  which  ignites  the 
phosphorus.  Here  there  is  a  double  transfer  of  energy.  The 
muscular  energy  of  the  arm  is  converted  into  mechanical  en- 
ergy in  the  moving  match,  and  a  part  of  this  into  heat  by  the 
friction. 

Before  matches  were  invented,  the  flint  and  steel  were  used 
for  the  same  purpose.  The  steel  was  struck  against  the  flint, 
and  the  spark  obtained  was  caught  in  tinder.  A  part  of  the 
mechanical  energy  of  the  steel  appeared  as  heat  in  the  spark. 

Indians  are  said  to  obtain  fire  by  vigorously  rubbing  to- 
gether two  pieces  of  dry  wood.  In  this  case,  too,  the  heat  is 
nothing  but  mechanical  energy  appearing  in  a  new  form. 

Iron  can  be  heated  red-hot  by  hammering  it.  And,  gen- 
erally, heat  is  developed  by  friction  and  percussion. 

4.  A II  Mechanical  Energy  is  ultimately  converted  into  Heat.  — 
When  a  falling  body  strikes  the  earth,  it  becomes  heated.  In 
this  case  the  whole  energy  of  the  body  is  converted  into  heat. 
When  bodies  are  rubbed  together,  their  energy,  as  we  have 
seen,  is  converted  into  heat. 

The  energy  of  a  running  stream  is  gradually  converted  into 
heat  by  the  friction  against  its  banks  and  bed  and  among  its 
particles.  If  it  is  made  to  turn  the  wheels  of  a  factory  on  its 
way,  the  rubbing  of  the  parts  of  the  machinery  against  each 
other  and  against  the  air,  together  with  the  various  kinds  of 
work  done  by  the  machinery,  converts  the  mechanical  energy 
of  the  water-wheel  into  heat. 

A  railway  train  is  really  stopped  by  the  conversion  of  its 
motion  into  heat.  When  this  has  to  be  done  quickly,  the 
change  is  hastened  by  increasing  the  friction  by  means  of  the 
brakes.  On  the  other  hand,  in  order  to  prevent  the  loss  of 
energy  while  the  train  is  in  motion,  the  axles  of  the  wheels  are 
kept  carefully  oiled,  that  they  may  turn  with  as  little  friction  as 
possible. 

When  unlike  substances  are  rubbed  together,  a  part  of  the 

energy  is  first  converted  into  electricity,  but  ultimately  into  heat. 

5.  When  Mechanical  Energy  is  converted  into  Heat,  the  Same 

Amount  of  Energy  always  gives  rise  to  the  Same  Amount  of 


360 


APPENDIX. 


Heat,  —  This  was  first  shown  by  Joule,  who  began  his  experi- 
ments in  1843  and  continued  them  till  1849.  He  converted 
mechanical  energy  into  heat  by  means  of  friction.  He  first  ex- 
amined cases  of  the  friction  of  solids  against  liquids.  The  ap- 
paratus used  for  this  purpose  is  shown  in  Figure  236.  B  is  a 
cylindrical  box  holding  the  liquid.  In  the  centre  of  the  box  is 


Fig.  236. 


an  upright  axis,  to  which  are  attached  eight  paddles  like  the 
one  shown  in  the  figure.  These  revolve  between  four  station- 
ary vanes,  which  prevent  the  liquid  from  being  carried  round. 
The  paddles  are  turned  by  means  of  the  cord  r  and  the  weight 
W.  The  size  of  the  weight  is  such  that  it  descends  without 
acquiring  any  velocity,  and  hence  all  its  energy  is  expended  in 
the  friction  of  the  paddles.  The  degree  to  which  the  liquid 
becomes  heated  by  the  friction  is  shown  by  a  thermometer 
at  /.  Knowing  the  weight  of  the  liquid,  its  specific  heat,  and 
the  rise  of  temperature  during  the  experiment,  the  amount  of 
heat  generated  can  be  readily  calculated. 

With  this  machine  Joule  found  that,  whatever  the  liquid  he 
used,  a  weight  of  one  pound  falling  through  772  feet,  or  772 
pounds  falling  one  foot,  generated  heat  enough  to  raise  one 
pound  of  water  one  degree  Fahrenheit  in  temperature,  or  one 
unit  of  heat,  as  it  is  called. 


APPENDIX.  361 

He  also  found  that,  when  solids  were  rubbed  together  by  the 
action  of  a  falling  weight,  one  pound  falling  through  772  feet 
generated  a  unit  of  heat.  In  this  experiment  iron  discs  were 
made  to  rotate  together,  one  against  the  other,  in  a  vessel  of 
mercury. 

If  a  metallic  disc  be  put  into  rapid  rotation  and  then  brought 
between  the  poles  of  a  powerful  electro-magnet,  it  soon  comes 
to  rest.  It  will  now  be  found  very  difficult  to  turn  it,  and  it 
becomes  heated  as  it  rotates.  Joule  found  in  this  case,  as  in 
the  others,  that,  if  the  disc  is  turned  by  a  falling  weight,  one 
pound  descending  772  feet  generates  a  unit  of  heat. 

The  force  necessary  to  raise  one  pound  one  foot  is  called  a 
foot-pound;  and  this  is  the  same  force- which  a  pound  acquires 
in  falling  one  foot  from  a  state  of  rest. 

We  see,  then,  that  when  mechanical  energy  is  converted  into 
heat,  the  same  amount  of  energy  always  gives  rise  to  the  same 
amount  of  heat,  and  that  772  foot-pounds  of  mechanical  force 
are  equivalent  to  one  unit  of  heat.  For  this  reason,  we  call 
772  foot-pounds  the  mechanical  equivalent  of  heat. 

6.  Heat  may  be  converted  into    Mechanical  Energy.  —  The 
steam-engine  is  a  contrivance  for  converting  heat  into  mechan- 
ical energy.     The  heat  converts  the  water  into  steam,  and  gives 
to  this  steam  an  expansive  force  ;  and  this  expansive  force  is 
made  to  move  a  piston,  as  has  already  been  explained  (Part  I., 
pages  loo-  102). 

The  animal  body  is  a  machine  for  converting  the  molecular 
energy  developed  by  affinity  into  mechanical  energy. 

7.  The  Same  Amount  of  Heat  always  gives  rise  to  the  Same 
Amount  of  Mechanical  Energy.  —  In  Figure  237,  C  is  a  box  a 

Fig  237  *°ot  S(luare>  Suppose  a  a  to  be  a  partition  one 
i  foot  from  the  bottom,  so  as  to  shut  in  a  cubic 
foot  of  air.  Suppose  this  partition  to  be  immov- 
able, and  the  air  beneath  to  be  heated.  Its 
elastic  force  will  be  increased,  but  it  cannot  ex- 
pand. We  will  next  suppose  that  a  a  is  mov- 
able, but  without  weight,  and  that  the  air  beneath 
is  heated  as  before.  On  raising  its  temperature 
490°  its  volume  will  be  doubled,  and  a  a  will  of 
course  be  raised  one  foot  to  b  b.  In  raising  a  a 


362 


APPENDIX. 


one  foot  it  has  had  to  raise  the  air  above  it.  Now  this  air 
presses  with  a  force  of  15  pounds  upon  every  square  inch,  or 
15  X  144  =  2,160  pounds  upon  the  whole  surface.  From  the 
specific  heat  of  air,  we  know  that  to  raise  the  temperature  of 
a  cubic  foot  of  air  490°,  when  it  is  free  to  expand,  9.5  units  of 
heat  are  required. 

But  we  have  seen  that  a  part  of  the  heat  which  enters  a  body 
is  used  in  expanding  it,  and  a  part  in  raising  its  temperature. 
In  the  above  experiment,  how  much  heat  is  used  in  raising  the 
temperature  ?  This  is  equivalent  to  asking  how  much  heat  is 
required  to  raise  the  cubic  foot  of  air  490°  when  it  is  not 
allowed  to  expand.  We  have  learned  that  the  computed  ve- 
locity of  sound  in  air  is  less  than  its  observed  velocity,  and  that 
this  is  owing  to  the  heat  developed  in  the  compressed  portion 
of  the  sound-wave.  From  the  ratio  between  the  observed  and 
the  computed  velocity,  it  is  found  that  the  specific  heat  of  air 
when  free  to  expand  must  be  1.42  of  its  heat  when  not  allowed 
to  expand.  Hence  the  heat  required  to  raise  the  temperature 
of  the  cubic  foot  of  air  490°,  when  it  is  not  allowed  to  expand, 
is  found  by  the  following  proportion  to  be  6.7  units  :  — 

1.42  :  i  =  9.5  :  6.7. 

The  amount  of  heat,  then,  used  in  expanding  the  air — that 
is,  in  raising  2,160  pounds  one  foot  high  — is  2.8  units.  Divid- 
ing 2,160  by  2.8,  we  get  772,  nearly. 

Since  there  is  no  cohesion  among  the  particles  of  air,  the 
whole  expansive  force  is  used  in  raising  the  weight. 

We  see,  then,  that  772  foot-pounds  of  mechanical  force  are 
equivalent  to  a  unit  of  heat,  and  that  a  unit  of  heat  is  equivalent 
to  772  foot-pounds  of  mechanical  force. 

We  have  seen  that  merely  to  melt  a  pound  of  ice  at  a 
temperature  of  32°  Fahrenheit  requires  143  units  of  heat,  which 
is  equivalent  to  the  force  required  to  lift  110,396  pounds,  or 
about  55  tons,  a  foot  high.  And  to  convert  a  pound  of  boiling 
water  into  steam  requires  967  units  of  heat,  equivalent  to  the 
force  required  to  lift  746,524  pounds,  or  about  373  tons,  a  foot 
high.  The  force  of  gravity  is  almost  as  nothing  compared  with 
this  molecular  force. 

The  strength  of  affinity  is  shown  by  the  amount  of  heat  de- 


APPENDIX.  363 

veloped  by  the  combination  of  oxygen  and  hydrogen.  It  is 
found  that,  when  oxygen  unites  with  one  pound  of  hydrogen, 
61,000  units  of  heat  are  generated.  Hence  the  force  which 
has  combined  the  two  gases  is  equal  to  61,000  X  7?2  = 
47,092,000  foot-pounds,  or  the  force  necessary  to  raise  23,546 
tons  a  foot  high,  or  to  throw  one  ton  to  a  height  of  more  than 
four  miles.  A  pound  of  carbon,  in  combining  with  oxygen, 
gives  out  about  14,500  units  of  heat,  equivalent  to  11.194,000 
foot-pounds.  We  see,  then,  that  the  force  even  of  cohesion  is 
insignificant  compared  with  that  of  affinity. 

8.  Energy  may  be  transmuted,  but  not  destroyed.  —  We  have 
now  seen  that  mechanical  motion  may  be  converted  into  the 
molecular  motions  of  heat  and  electricity,  and  that  these  molec- 
ular motions  may  be  converted  into  mechanical  motion. 

Energy,  like  matter,  may  assume  a  great  variety  of  forms  ; 
but,  like  matter,  it  is  wholly  indestructible. 

9.  Source  of  Energy.  —  If  left  to  itself,  affinity  would  soon 
bring  all  dissimilar  atoms  together,  and  lock  them  up  in  com- 
pounds ;  cohesion  would  bring  all  the  molecules  of  these  com- 
pounds together,  and  lock  them  up  in  -solids ;  and  gravity 
would  bring  all  these  solids  together,  and  hold  them  in  its  iron 
grasp ;  while  the  heat  developed  by  these  forces  would  be 
radiated  into  space,  and  our  earth  become  one  dreary  waste, 
void  of  all  signs  of  life  and  activity.  What,  then,  is  the  source 
of  the  energy  which  is  thus  manifesting  itself  in  Protean  forms  ? 

Let  us  consider,  first,  the  energy  developed  by  gravity. 
This  energy  is  seen  in  the  winds,  the  falling  rain,  and  running 
streams.  The  atmosphere  on  each  side  of  the  equator  is  an 
immense  wheel.  The  side  of  this  wheel  next  the  equator  is 
continually  expanded,  and  thus  made  lighter,  by  the  heat  of  the 
sun.  Hence  gravity  pulls  down  the  colder  and  heavier  side  in 
the  polar  regions,  and  thus  the  wheel  is  made  to  turn.  Were 
it  not  for  the  sun's  heat,  it  would  soon  come  to  rest. 

Again,  the  heat  of  the  sun  evaporates  the  waters  of  the 
ocean,  and  in  their  gaseous  state  they  are  swept  round  with 
the  atmospheric  wheel  till  they  come  to  colder  regions,  where 
they  are  condensed,  and  fall  to  the  earth  as  rain,  and  flow  to 
the  ocean  in  rivers.  It  is  due,  then,  to  the  heat  which  comes 
to  the  earth  in  the  sunbeam,  that  gravity  cap  thus  unceasingly 
manifest  its  energy. 


364  APPENDIX. 

The  energy  of  chemical  affinity  which  is  manifested  in  heat, 
light,  and  muscular  force  is  developed  by  its  action  between 
oxygen  and  carbon.  How  are  these  elements  separated  from 
carbonic  acid,  so  that  they  may  be  reunited  by  affinity  ? 

Place  a  leafy  plant  in  a  glass  vessel,  and  let  a  current  of  car- 
bonic acid  stream  over  it  in  the  dark,  and  no  change  takes 
place.  Let  the  same  gas  stream  over  the  plant  in  the  sunshine, 
and  a  part  of  it  will  disappear,  and  be  replaced  by  oxygen. 
When  acted  upon  by  the  sunbeams,  leaves  of  plants  remove 
carbonic  acid  from  the  air,  separate  its  carbon  and  oxygen, 
retain  the  former,  and  give  the  latter  back  to  the  air.  When 
plants  are  consumed  by  combustion  in  our  furnaces,  and  by 
respiration  in  our  bodies,  this  oxygen  combines  with  carbon 
and  develops  energy,  which  appears  as  mechanical  force  in  our 
engines,  and  as  muscular  force  in  our  bodies. 

In  the  summer,  when  more  sunshine  than  we  need  is  poured 
upon  the  earth,  a  part  of  it  is  absorbed  by  the  leaves  of  plants, 
and  used  to  decompose  carbonic  acid,  to  build  up  the  varied 
forms  of  vegetable  life.  In  this  way,  the  forests  and  the  fields 
become  vast  storehouses  of  force  which  has  been  gathered  from 
the  sunbeam.  When,  therefore,  we  burn  fuel  in  our  stoves  and 
food  in  our  bodies,  the  light,  heat,  and  muscular  force  de- 
veloped are  only  the  reappearance  in  another  form  of  the  sun- 
beams stored  up  in  plants. 

But  this  process  of  gathering  force  from  the  sunlight  has 
been  going  on  for  ages  ;  and  when  we  burn  anthracite  or 
bituminous  coal,  we  are  merely  releasing  the  sunbeams  im- 
prisoned in  plants  which  grew  upon  the  earth  before  it  became 
the  dwelling-place  of  man. 

The  energy  of  affinity,  then,  like  that  of  gravity,  is  nothing 
but  transmuted  sunshine. 

The  only  form  of  energy  known  to  us  which  does  not  come 
to  the  earth  in  the  sunbeam  is  that  developed  by  the  ebb  and 
flow  of  the  tidal  wave.  This  wave  is  dragged  round  the  earth 
mainly  by  the  attraction  of  the  moon  ;  and  it  acts  as  a  brake 
upon  the  earth's  rotation,  since  it  is  drawn  from  east  to  west 
while  the  earth  is  turning  from  west  to  east.  The  energy  of 
this  wave,  then,  is  developed  at  the  expense  of  the  earth's 
motion  on  its  axis  ;  and  it  must  tend  to  retard  this  motion, 


APPENDIX.  365 

though  to  so  slight  a  degree  that  the  observations  of  thou- 
sands of  years  have  not  served  to  make  it  appreciable. 

10.  The  Amount  of  Heat  given  out  by  the  Sim.  —  Making 
allowance  for  the  heat  absorbed  by  the  atmosphere,  it  has  been 
calculated  that  the  amount  received  by  the  earth  during  a  year 
would  be  sufficient  to  melt  a  layer  of  ice  100  feet  thick  and  cov- 
ering the  whole  earth.     But  the  sun  radiates  heat  into  space  in 
every  other  direction  as  well  as  towards  the  earth  ;  and  if  we 
conceive  a  hollow  sphere  to  surround  the  sun  at  the  distance  of 
the  earth,  our  planet  would  cover  only      ^Locoo  of  its  surface. 
Hence  the  sun  radiates  into  space  2,300,000,000  times  as  much 
heat  as  the  earth  receives.     Sir  John  Herschel  has  calculated 
that  if  a  cylinder  of  ice  45  miles  thick  were  darted  into  the  sun 
with  the  velocity  of  light  (190,000  miles  a  second),  it  might  be 
melted  by  the  heat  radiated  by  the  sun,  without  lowering  the 
temperature  of  the  sun  itself. 

11.  Source  of  the  Surfs  Heat.  —  It  has  been  supposed  by 
some  that  the  materials  of  the  sun  are  undergoing  combustion, 
and  that  this  combustion  develops  the  light  and  heat  which  it 
sends  forth.     There  are,  however,  no  substances  known  to  us 
whose  burning  would  produce  so  much  heat  for  so  long  a  time 
as  we  know  the  sun  has  been  shining.     Carbon  is  one  of  the 
most  combustible  substances  with  which  we  are  acquainted  ; 
but  if  the  sun,  large  as  he  is,  were  a  mass  of  pure  carbon,  and 
were  burning  at  a  rate  sufficient  to  produce  the  light  and  heat 
that  he  is  giving  out,  he  would  be  utterly  consumed  in  5,000 
years.     It  seems  hardly  possible,  then,  that  the  solar  light  and 
heat  can  be  generated  by  ordinary  combustion. 

One  of  the  most  satisfactory  theories  of  the  origin  of  the 
solar  heat  is  that  developed  in  1848  by  a  German  physician, 
Mayer,  and  known  as  the  meteoric  theory. 

We  have  seen  that  a  pound-weight  which  has  fallen  through 
772  feet  will,  when  its  motion  is  arrested,  generate  a  unit  of 
heat.  Now,  we  know  that  a  body  falling  that  distance  will 
acquire  a  velocity  of  about  223  feet  a  second.  Hence  a  pound 
ball  moving  with  a  velocity  of  223  feet  a  second  will  generate  a 
unit  of  heat  when  its  motion  is  arrested.  We  know,  too,  that 
the  velocity  with  which  a  falling  body  strikes  the  ground  is  in 
proportion  to  the  square  root  of  the  height  from  which  it  falls ; 


3  66  APPENDIX. 

that  is,  in  order  to  double  or  treble  its  velocity,  a  body  must 
fall  from  four  or  nine  times  the  height.  A  pound  ball,  then, 
moving  with  a  velocity  of  twice  223  feet  a  second  will  be  able 
to  generate  4  units  of  heat ;  one  moving  with  thrice  this 
velocity,  9  units  of  heat  ;  and  so  on.  When,  therefore,  we 
know  the  weight  of  a  body  and  the  speed  with  which  it  is 
moving,  we  can  easily  calculate  how  much  heat  will  be  gen- 
erated on  stopping  it. 

Were  tfie  earth's  motion  arrested,  its  elements  would  melt 
with  fervent  heat,  and  most  of  them  would  be  converted  into 
v'apor.  Were  the  earth  to  fall  into  the  sun,  the  heat  generated 
by  the  shock  would  be  sufficient  to  keep  up  the  solar  light  and 
heat  for  95  years.  We  know  that  countless  swarms  of  meteoric 
bodies  are  revolving  in  rings  about  the  sun,  and  that  they  must 
be  moving  in  a  resisting  medium.  If  so,  they  must  eventually 
be  drawn  into  the  sun,  and,  from  the  velocity  with  which  they 
must  strike,  it  has  been  shown  that  they  could  fall  in  sufficient 
numbers  to  generate  all  the  light  and  heat  of  the  sun,  without 
increasing  his  magnitude  enough  to  be  detected,  since  accurate 
measures  of  his  diameter  were  first  made. 

"  Solar  light  and  solar  heat  lie  latent  in  the  force  which  pulls 
an  apple  to  the  ground.  The  potential  energy  of  gravitation 
was  the  original  form  of  all  the  energy  in  the  universe.  As 
surely  as  the  weights  of  a  clock  run  down  to  their  lowest  posi- 
tion, from  which  they  can  never  rise  again  unless  fresh  energy 
is  communicated  to  them  from  some  source  not  yet  exhausted, 
so  surely  must  planet  after  planet  creep  in,  age  by  age,  towards 
the  sun.  When  each  comes  within  a  few  hundred  thousand 
miles  of  his  surface,  if  he  is  still  incandescent,  it  must  be 
melted  and  driven  into  vapor  by  radiant  heat.  Nor,  if  he  be 
crusted  over  and  become  dark  and  cool  externally,  can  the 
doomed  planet  escape  its  fiery  end.  If  it  does  not  become  in- 
candescent, like  a  shooting-star,  by  friction  in  its  passage 
through  his  atmosphere,  its  first  graze  on  his  surface  must  pro- 
duce a  stupendous  flash  of  light  and  heat.  It  may  be  at  once, 
or  it  may  be  after  two  or  three  bounds  like  a  cannon-shot 
ricochetting  on  a  surface  of  earth  or  water,  the  whole  mass 
must  be  crushed,  melted,  and  evaporated  by  a  crash,  generat- 
ing in  a  moment  some  thousands  of  times  as  much  heat  as  a 
coal  of  the  same  size  would  produce  by  burning."  (Tyndall.) 


APPENDIX.  367 

12.  The  Nebular  Hypothesis.  —  According   to  Laplace,  the 
material  of  our  solar  system  was  once  a  nebulous  mass  of  ex- 
treme tenuity,  and  the  sun,  moon,  and  planets  were  formed  by 
its  gradual  condensation.     Let  us  suppose   such   a   nebulous 
mass  slowly  rotating,  and  gradually  cooling  by  radiation  into 
space.     As  it  cools,  it  must  begin  to  contract ;  and  as  it  con- 
tracts, its  rotation  must  be  quickened,  since  the  matter  at  the 
surface  must  be  moving  faster  than  nearer  the  centre.     It  thus 
goes  on  contracting  and  rotating  faster  and  faster,  until  the 
centrifugal  tendency  becomes  so  great  that  cohesion  and  grav- 
ity can  no  longer  hold  it  together.     A  ring  is  then  detached 
from   the  circumference,  which  continues   to    rotate  by  itself. 
The  central  mass  goes  on  contracting  and  rotating  with  ever- 
increasing  velocity,  until  a  second  ring  is  thrown  off.     In  this 
way,  ring  after  ring  is  detached,  and  all  these  rings  continue  to 
rotate  round  the  central  mass  in  the  same  direction.     But  the 
rings  themselves  would  go  on  condensing,  and  at  last   they 
would  be  likely  to  break  up,  each  forming  one  or  several  glob- 
ular masses.     These  would,  of  course,  all  revolve  about  the 
central   mass   in  the   same  direction,  and   their  condensation 
would  cause  them  to  rotate  on   their  axes  ;  and  it  has  been 
proved  that,  with  the  exception  of  one  or  two  of  the  outer  ones, 
they  must  all  rotate  on  their  axes  in  the   same  direction  in 
which  they  revolve  in  their  orbits. 

But  as  these  masses  condensed,  their  rotation  would  be  ac- 
celerated, and  they  would  be  very  likely  to  throw  off  rings, 
which  would  either  .remain  as  rings,  or  be  condensed  into 
globes. 

The  central  mass,  of  course,  forms  the  sun  ;  the  rings  which 
it  throws  off,  the  planets  ;  and  the  rings  thrown  off  by  the 
planets,  the  moons.  In  the  case  of  Saturn,  a  part  of  the  rings 
still  remain  uncondensed,  while  a  part  appear  as  moons. 

The  rings  thrown  off  by  the  central  mass  usually  condensed 
into  one  body,  but,  in  the  case  of  the  minor  planets  and  the 
meteoric  rings,  into  many. 

13.  Helmholtz's    Theory   of  Solar  Heat.  —  Helmholtz    has 
made  the  nebular  hypothesis  the  basis  of  his  theory  of  solar 
heat,  an  account  of  which  is  given  by  Tyndall  as  follows  :  — 

"  He    starts    from  tne  nebular  hypothesis  of  Laplace,  and, 


368  APPENDIX. 

assuming  the  nebulous  matter  in  the  first  instance  to  have  been 
of  extreme  tenuity,  he  determines  the  amount  of  heat  generated 
by  its  condensation  to  the  present  solar  system.  Supposing 
the  specific  heat  of  the  condensing  mass  to  be  the  same  as  that 
of  water,  then  the  heat  of  condensation  would  be  sufficient  to 
raise  their  temperature  28,000,000°  Centigrade.  By  far  the 

greater  part  of  this  heat  was  wasted  ages  ago  in  space 

Helmholtz  supposes  this  condensation  to  continue  ;  that  a  vir- 
tual falling  down  of  the  superficial  portions  of  the  sun  towards 
the  centre  still  takes  place,  a  continual  development  of  heat 
being  the  result.  However  this  may  be,  he  shows  by  calcula- 
tion that  the  shrinking  of  the  sun's  diameter  by  .0001  of  its 
present  length  would  generate  an  amount  of  heat  competent  to 
cover  the  solar  emission  for  2,000  years  ;  while  the  shrinking  of 
the  sun  from  its  present  mean  density  to  that  of  the  earth 
would  have  its  equivalent  in  an  amount  of  heat  competent  to 
cover  the  present  solar  emission  for  17,000,000  of  years. 

"'But,'  continues  Helmholtz,  'though  the  store  of  our 
planetary  system  is  so  .immense  that  it  has  not  been  sensibly 
diminished  by  the  incessant  emission  which  has  gone  on  during 
the  period  of  man's  history,  and  though  the  time  which  must 
elapse  before  a  sensible  change  in  the  condition  of  our  plane- 
tary system  can  occur  is  totally  beyond  our  comprehension,  the 
inexorable  laws  of  mechanics  show  that  this  store,  which  can 
only  suffer  loss  and  not  gain,  must  finally  be  exhausted.  Shall 
we  terrify  ourselves  by  this  thought?  We  are  in  the  habit  of 
measuring  the  greatness  of  the  universe,  and  the  wisdom  dis- 
played in  it,  by  the  duration  and  the  profit  which  it  promises  to 
our  own  race  ;  but  the  past  history  of  the  earth  shows  the  insig- 
nificance of  the  interval  during  which  man  has  had  his  dwelling 
here.  What  the  museums  of  Europe  show  us  of  the  remains 
of  Egypt  and  Assyria  we  gaze  upon  with  silent  wonder,  in 
despair  of  being  able  to  carry  back  our  thoughts  to  a  period  so 
remote.  Still,  the  human  race  must  have  existed  and  multi- 
plied for  ages  before  the  Pyramids  could  have  been  erected. 
We  estimate  the  duration  of  human  history  at  6,000  years  ;  but, 
vast  as  this  time  may  appear  to  us,  what  is  it  in  comparison 
with  the  period  during  which  the  earth  bore  successive  series 
of  rank  plants  and  mighty  animals,  but  no  men  ?  —  periods 


APPENDIX.  369 

during  which,  in  our  own  neighborhood  (Konigsberg),  the  am- 
ber-tree bloomed,  and  dropped  its  costly  gum  on  the  earth 
and  in  the  sea ;  when  in  Europe  and  North  America  groves 
of  tropical  palms  flourished,  in  which  gigantic  lizards,  and,  after 
them,  elephants,  whose  mighty  remains  are  still  buried  in  the 
earth,  found  a  home.  Different  geologists,  proceeding  from 
different  premises,  have  sought  to  estimate  the  length  of  the 
above  period,  and  they  set  it  down  from  one  to  nine  millions 
of  years.  The  time  during  which  the  earth  has  generated 
organic  beings  is  again  small  compared  with  the  ages  during 
which  the  world  was  a  mass  of  molten  rocks.  The  experiments 
of  Bischof  upon  basalt  show  that  our  globe  would  require  350 
millions  of  years  to  cool  down  from  2,000°  to  200°  Centigrade. 
And  with  regard  to  the  period  during  which  the  first  nebulous 
masses  condensed,  to  form  our  planetary  system,  conjecture 
must  entirely  cease.  The  history  of  man,  therefore,  is  but  a 
minute  ripple  in  the  infinite  ocean  of  time.  For  a  much  longer 
period  than  that  during  which  he  has  already  occupied  this 
world,  the  existence  of  a  state  of  inorganic  nature,  favorable 
to  man's  continuance  here,  seems  to  be  secured  ;  so  that  for 
ourselves,  and  for  long  generations  after  us,  we  have  nothing  to 
fear.  But  the  same  forces  of  air  and  water,  and  of  the  volcanic 
interior,  which  produced  former  geologic  revolutions,  burying 
one  series  of  living  forms  after  another,  still  act  upon  the  earth's 
crust.  They,  rather  than  those  distant  cosmical  changes  of 
which  we  have  spoken,  will  put  an  end  to  the  human  race,  and 
perhaps  compel  us  to  make  way  for  new  and  more  complete 
forms  of  life,  as  the  lizard  and  the  mammoth  have  given  way  to 
us  and  our  contemporaries.'  " 

Mayer's  theory  is  evidently  not  inconsistent  with  that  of 
Helmholtz,  but  supplementary  to  it.  The  former  merely  as- 
sumes that  the  meteors  and  planets,  which  were  thrown  off 
from  the  nebulous  mass  as  it  condensed,  are  slowly  falling  into 
it  again.  When  these  shall  all  have  fallen  into  it  and  the  con- 
densation shall  have  ceased,  our  sun  will  cease  to  shine,  like 
many  other  stars  which  have  disappeared  from  the  heavens. 
16*  x 


NOTES. 

PART    FIRST. 
I. 

ANOTHER  way  to  find  the  specific  gravity  of  a  liquid  is  the 
following.  Fill  a  small  bottle  accurately  with  water,  and  then 
with  the  liquid,  and  find  the  weight  of  each  ;  then  divide  the 
weight  of  the  liquid  by  the  weight  of  the  water,  and  the  quotient 
will  be  the  specific  gravity  required. 

A  specific  gravity  bottle  is  a  bottle  which  is  made  to  hold  a 
definite  weight  of  water,  as  1,000  grains.  If  it  holds  790  grains 
of  alcohol,  the  specific  gravity  of  the  alcohol  is  evidently  .79 ; 
if  it  holds  i, 860  grains  of  sulphuric  acid,  the  specific  gravity  of 
the  acid  is  1.86  ;  and  so  on. 

Again,  since  the  weight  which  a  body  loses  when  immersed 
in  a  liquid  is  equal  to  the  weight  of  its  own  bulk  of  that  liquid 
(23),  we  can  find  the  specific  gravity  of  a  liquid  by  dividing  the 
weight  which  a  body  loses  in  that  liquid  by  the  weight  which 
:.t  loses  in  water.  Thus,  if  a  piece  of  copper  loses  200  grains 
when  weighed  in  water,  and  158  grains  when  weighed  in  alco- 
hol, the  specific  gravity  of  the  alcohol  is  equal  to  158  divided 
:•-••  200,  or  .79. 


II. 

WHEN  we  know  the  velocity  a  body  acquires  in  falling  through 
a  certain  distance  a,  and  we  wish  to  know  what  velocity  it  will 
acquire  in  falling  through  any  other  distance  b,  divide  the  dis- 
tance b  by  a,  extract  the  square  root  of  the  quotient,  and  mul- 
tiply the  velocity  the  body  acquires  in  falling  through  the 


APPENDIX.  371 

distance  a  by  the  number  thus  obtained.  If,  on  the  other  hand, 
we  wish  to  know  how  far  the  body  must  fall  to  acquire  any 
velocity  c,  divide  the  velocity  c  by  the  velocity  a  body  acquires 
in  falling  through  the  distance  #,  square  the  quotient,  and  mul- 
tiply the  distance  a  by  this  number. 

PROBLEMS. 

1.  A  body  in  falling  from  a  state  of  rest  through  4.9  metres 
acquires  a  velocity  of  9.8  metres.    Through  what  distance  must 
it  fall  to  acquire  a  velocity  of  39.2  metres  ? 

2.  To  acquire  a  velocity  of  88.2  metres  ? 

3.  To  acquire  a  velocity  of  125  metres  ? 

4.  To  acquire  a  velocity  of  396  metres  ? 

5.  What  velocity  does  a  body  acquire  in  falling  from  a  state 
of  rest  through  19.6  metres? 

6.  In  falling  through  44.1  metres  ? 

7.  In  falling  through  340  metres  ? 

8.  A  body  falls  from  a  height  of  60  metres.   With  what  ve- 
locity does  it  reach  the  earth  ? 

9.  How  long  is  the  body  in  falling  to  the  earth  ? 

10.  How  long  will  it  take  a  body  to  fall  from  a  state  of  rest 
through  i, 1 88  metres? 

11.  A  cannon  ball  is   fired   horizontally  from  the  top  of  a 
tower  60  metres  high.     How  long  will  the  ball  remain  in  the 
air? 

FRENCH   WEIGHTS   AND   MEASURES. 
gg="  The  English  equivalents  given  below  are  those  which 
were  established  by  Congress,  in  July,  1866,  and  are  sufficient- 
ly accurate  for  all  practical  purposes. 

TABLE  OF  LINEAR  MEASURE. 


10  millimetres 

=  i  centimetre 

=      0-3937  inch. 

10  centimetres 

=  I  decimetre 

=      3-937     " 

10  decimetres 

=  i  metre 

=    39-37      " 

10  metres 

=  i  decametre 

=  393-7 

10  decametres 

=  i  hectometre 

=  328  ft.   i  inch. 

10  hectometres 

=  I  kilometre 

=  3280  "  10     " 

372 


APPENDIX. 


TABLE  OF  MEASURES  OF  SURFACE. 

=  1 19.6  square  yards. 
=      2.471  acres. 

The  centiare  is  a  square  metre,  and  is  equal  to  1,550  square 
inches. 


100  centiares 
100  ares 


=   I  are 
=  i  hectare 


TABLE  OF  MEASURES  OF  CAPACITY. 

10  millilitres  = 

10  centilitres  = 

10  decilitres  = 

10  litres  = 

10  decalitres  = 

10  hectolitres  = 

The  kilolitre  is  a  cubic  metre,  and  is  also  called  a  stere. 
decastere=  10  steres. 


centilitre 

=      0.6102  cubic  inches. 

decilitre 

=        6.1022      "           " 

litre 

=      1.0567  wine  quarts. 

decalitre 

=      2.6417     "    gallons. 

hectolitre 

=    26.417       « 

kilolitre 

=  264.17        "         " 

The 


TABLE  OF  WEIGHTS. 

i  o  milligrammes    =  I  centigramme  =    0.1543  grains. 

10  centigrammes    =  I  decigramme  =    1.5432    " 

10  decigrammes     =  i  gramme  =15.432      " 

10  grammes  =  i  decagramme  =    0.3527  oz.  avoirdupois. 

10  decagrammes    =  i  hectogramme  =    3-5274  "  " 

10  hectogrammes  =  i  kilogramme  =    2.2046  pounds  " 

The  millier  or  tonneau  is  equal  to  1,000,000  grammes,  or 
2204.6  pounds  avoirdupois. 

NOTE.  The  names  of  the  higher  orders  of  units,  or  the  multiples  of 
the  standard  unit,  are  formed  from  the  name  of  the  standard  unit, 
(the  metre,  litre,  etc.)  by  means  of  prefixes  taken  from  the  Greek 
numerals  ;  namely,  deca-  (10),  hecto-  (100),  kilo-  (1,000). 

The  names  of  the  lower  orders  of  units,  or  the  subdivisions  of  the 
standard  unit,  are  formed  in  a  similar  manner  by  means  of  prefixes 
taken  from  th«>'  Latin  numerals ;  namely,  deci-  (10),  centi-  (100),  milli- 
(1,000). 


PART    SECOND. 


1.  (page   23.)   For  other  methods  of  illustrating  the  forma- 
tion of  nodes  see  TyndalFs  Lectures  on  "  Sound." 

2.  (page  79.)  Sensitive  Naked  Flames.  —  Professor  Leconte 
of  this  country  was  the  first  to  observe  that  ordinary  gas-flames, 
even  when  not  enclosed  in  tubes,  are  sensitive  to  sound.     He 
gives  the  following  account  of  his  observations  at  a  musical 
party  :  "  Soon  after  the  music  commenced,  I  observed  that  the 
flame  exhibited  pulsations  which  were  exactly  synchronous  with 
the  audible   beats.     This   phenomenon   was   very   striking  to 
every  one  in  the  room,  and  especially  so  when  the  strong  notes 
of  the  violoncello  came  in.     It  was  exceedingly  interesting  to 
observe  how  perfectly  even  the  trills  of  this  instrument  were 
reflected  on  the  sheet  of  flame.     A  deaf  man  might  have  seen 
the  harmony.     As  the  evening  advanced,  and  the  diminished 
consumption  of  gas  in  the  city  increased  the  pressure,  the  phe- 
nomenon  became   more   conspicuous.      The  jumping  of  the 
flame  gradually  increased,   became   somewhat  irregular,  and, 
finally,  it  began  to  flare  continuously,  emitting  the  character- 
istic sound  indicating  the  escape  of  a  greater  amount  of  gas 
than   could   be   properly  consumed.      I    then   ascertained  by 
experiment,  that  the  phenomenon  did  not  take  place  unless  the 
discharge  of  gas  was  so  regulated  that  the  flame  approximated 
to  the  condition  of  flaring.     I  likewise  determined,  by  experi- 
ment, that  the  effects  were  not  produced  by  jarring  or  shaking 
the  floor  and  walls  of  the  room  by  means  of  repeated  concus- 
sions.    Hence  it  is  obvious  that  the  pulsations  of  the  flame 
were  not  owing  to  indirect  vibrations  propagated  through  the 
medium  of  the  walls  of  the  room  to  the  burning  apparatus,  but 
must  have  been  produced  by  the  direct  influence  of  aerial  sono- 
rous pulses  on  the  burning  jet."  * 

*  Philosophical  Magazine,  March,  1858. 


3  74  APPENDIX. 

The  significant  remark,  that  the  jumping  of  the  flame  was 
not  observed  until  it  was  near  flaring,  suggests  t]?e  means  of 
repeating  the  experiments  of  Dr.  Leconte ;  while  a  more  inti- 
mate knowledge  of  the  conditions  of  success  enable  us  to  yary 
and  exalt  them  in  a  striking  manner. 

It  will  be  noticed  in  the  above  account  that  the  flame  be- 
comes more  sensitive  when  it  is  near  flaring. 

Figure  238  represents  the  flame  of  a  common  fish-tail  burner. 

Fig.  238.  Fig.  239. 


When  this  flame  is  not  near  flaring  it  is  not  at  all  sensitive  to 
sound.  If,  however,  we  turn  on  the  gas  until  the  flame  is  on 
the  point  of  flaring,  and  sound  a  whistle  near  it,  the  flame  takes 
the  form  shown  in  Figure  239.  With  a  bat's-wing  burner  the 
result  is  the  same. 

By  using  burners  of  suitable  forms,  flames  may  be  obtained 
which  are  much  more  sensitive  than  ordinary  gas-flames.  The 
simplest  burners,  and  those  which  show  the  sensitiveness  of 
the  flame  best,  can  be  made  by  drawing  out  small  glass  tubes 
into  a  fine  jet. 

Tyndall  gives  the  following  account  of  his  experiments  with 
a  tall  slender  flame  such  as  is  shown  in  Figure  240:  — 

"  The  flame  reaches  a  height  of  24  inches.     The  slightest  tap 


APPENDIX.  375 

on  a  distant  anvil  reduces  its  height  to  7-  inches.  When  I 
shake  this  bunch  of  keys  the  flame  is  violently  agitated,  and 
emits  a  loud  roar.  The  dropping  of  a  sixpence  into  a  hand 
already  containing  coin,  at  a  distance  of  20  yards,  knocks  the 
flame  down.  I  cannot  walk  across  the  floor  without 
Fig.  240.  agitating  the  flame.  The  creaking  of  my  boots  sets  it 
in  violent  commotion.  The  crumpling  or  tearing  of  a 
bit  of  paper,  or  the  rustle  of  a  silk  dress,  does  the 
same.  It  is  startled  by  the  patter  of  a  rain-drop.  I 
hold  a  watch  near  the  flame  ;  nobody  hears  its  ticks  ; 
but  you  all  see  their  effect  upon  the  flame.  At  every 
tick  it  falls.  The  winding  up  of  the  watch  also  pro- 
duces tumult.  The  twitter  of  a  distant  sparrow  shakes 
the  flame  down  ;  the  note  of  a  cricket  would  do  the 
same.  From  a  distance  of  30  yards  I  have  chirruped 
to  this  flame,  and  caused  it  to  fall  and  roar.  I  repeat 
a  passage  from  Spenser  :  — 

'  Her  ivory  forehead,  full  of  bounty  brave, 
Like  a  broad  table  did  itself  dispread, 
For  Love  his  lofty  triumphs  to  engrave, 

And  write  the  battles  of  his  great  godhead. 
All  truth  and  goodness  might  therein  be  read, 
Fig.  241.        jror  there  their   dwelling   was,    and  when   she 
*  spake, 

II,        Sweet  words,  like  dropping  honey  she  did  shed  ; 
IJIII          And  through  the  pearls  and  rubies  softly  brake 
A  silver  sound,  which  heavenly  music  seemed  to 
make.' 

The  flame  picks  out  certain  sounds  from  my 
utterance;  it  notices  some  by  the  slightest 
nod,  to  others  it  bows  more  distinctly,  to 
some  its  obeisance  is  very  profound,  while  to 
many  sounds  it  turns  an  entirely  deaf  ear. 

"  In  Figure  240  this  tall,  straight,  and  bril- 
liant flame  is  represented.  On  chirruping  to  it,  or  on  shaking 
a  bunch  of  keys  within  a  few  yards  of  it,  it  falls  to  the  size 
shown  in  Figure  241,  the  whole  length,  a  b,  of  the  flame  being 
suddenly  abolished.  The  light  at  the  same  time  is  practically 
destroyed,  a  pale  and  almost  non-luminous  residue  of  it  alone 
remaining. 


376  APPENDIX. 

"  We  have  called  this  the  vowel  flame,  because  the  different 
vowel  sounds  affect  it  differently.  We  have  already  learned 
how  these  sounds  are  formed  ;  that  they  differ  from  each  other 
through  the  admixture  of  higher  tones  with  the  fundamental 
one.  It  is  to  these  tones,  and  not  to  the  fundamental  one,  that 
our  flame  is  sensitive.  I  utter  a  loud  and  sonorous  u,  the 
flame  remains  steady ;  I  change  the  sound  to  o,  the  flame  quiv- 
ers ;  I  sound  E,  and  now  the  flame  is  strongly  affected.  I  utter 
the  words  boot,  boat,  and  beat  in  succession.  To  the  first  there 
is  no  response  ;  to  the  second,  the  flame  starts  ;  but  by  the 
third  it  is  thrown  into  greater  commotion  ;  the  sound  Ah  !  is  still 
more  powerful.  Did  we  not  know  the  constitution  of  vowel 
sounds  this  deportment  would  be  an  insoluble  enigma.  As  it 
is,  however,  the  flame  is  a  demonstrator  of  the  theory  of  vowel 
sounds.  It  is  most  sensitive  to  sounds  of  high  pitch  ;  hence 
we  should  infer  that  the  sound  Ah  !  contains  higher  notes 
than  the  sound  E  ;  that  E  contains  higher  notes  than  o  ;  and  o 
higher  notes  than  u.  I  need  not  say  that  this  agrees  perfectly 
with  the  analysis  of  Helmholtz. 

"  This  flame  is  peculiarly  sensitive  to  the  utterance  of  the 
letter  s.  If  the  most  distant  person  in  the  room  were  to  favor 
me  with  a  hiss,  the  flame  would  instantly  sympathize  with 
him.  A  hiss  contains  the  elements  that  most  forcibly  affect 
this  flame.  The  gas  issues  from  its  burner  with  a  hiss,  and  an 
external  sound  of  this  character  is  therefore  exceedingly  effec- 
tive. I  hold  in  my  hand  a  metal  box,  containing  compressed 
air.  I  turn  the  cock  for  a  moment,  so  as  to  allow  a  puff  to 
escape,  —  the  flame  instantly  ducks  down,  not  by  any  transfer 
of  air  from  the  box  to  the  flame,  for  I  stand  at  a  distance  which 
utterly  excludes  this  idea  ;  it  is  the  sound  that  affects  the  flame. 
I  send  a  man  to  the  most  distant  part  of  the  gallery,  where  he 
permits  the  compressed  air  to  issue  in  puffs  from  the  box ;  at 
every  puff  the  flame  suddenly  falls.  Thus  the  hiss  of  the  issu- 
ing air  at  the  one  orifice  precipitates  the  tumult  of  the  flame  at 
the  other. 

"  Finally,  I  place  this  musical  box  upon  the  table,  and  permit 
it  to  play.  The  flame  behaves  like  a  sentient  creature  ;  bow- 
ing slightly  to  some  tones,  but  courtesying  deeply  to  others." 

What  now  is  the  explanation  of  these  phenomena  ? 


APPENDIX.  377 

If  we  use  a  burner  with  a  single  circular  orifice  of  such  a 
size  that  it  requires  a  great  pressure  to  make  the  flame  flare, 
we  may,  by  turning  on  the  gas,  obtain  a  flame  15  or  20  inches 
long.  If  we  make  it  longer  and  larger,  it  will  at  length  begin 
to  quiver  and  finally  to  flare,  shortening  considerably  at  the 
same  time.  If  we  diminish  the  pressure  a  little,  so  as  to  bring 
the  flame  just  below  its  point  of  flaring,  it  shortens  on  sounding 
a  whistle  near  it,  exactly  as  it  did  when  the  pressure  was  in- 
creased. Like  the  singing  flame  which  was  started  by  the 
voice  (78),  it  stands  on  the  brink  of  a  precipice,  and  the 
proper  sound  pushes  it  over.  We  see,  then,  that  the  effect  of 
sound  upon  a  naked  flame  is  the  same  as  that  of  an  increase 
in  the  pressure  of  the  gas.  The  gas  in  escaping  from  the  ori- 
fice of  the  burner  encounters  friction,  and  when  the  pressure  of 
the  gas  is  sufficient,  the  stream  as  it  issues  is  thrown  into  vibra- 
tion. It  is  this  vibration  which  causes  the  flame  to  flare. 
Sonorous  pulses  of  the  proper  period  may  also  throw  the 
stream  of  gas  into  vibration,  and  thus  cause  the  flame  to  flare. 
In  a  word,  then,  the  flame  flares  because  the  gas  as  it  escapes 
from  the  burner  is  thrown  into  vibration,  and  it  may  thus  be 
thrown  into  vibration  by  increasing  the  pressure  of  the  gas  or 
by  the  action  of  sonorous  pulses  of  the  proper  period. 

It  has  been  found  that  liquid  jets,  as  well  as  gas  jets,  are 
sensitive  to  sound. 

3.  (page  1 01.)  Total  reflection  in  a  liquid  may  be  elegantly 
illustrated  by  the  following  experiment.     Near  the  bottom  of  a 
tall  vessel  a  round  hole  is  made  for  water  to  run  out ;  opposite 
this  hole  is  a  glass  plate,  through  which  a  beam  of  solar  or 
electric  light  is  admitted.     The  vessel  is  filled  with  water,  and 
the  outlet  opened.     The  beam  of  light  is  totally  reflected  from 
the  inner  surfaces  of  the  liquid  jet,  and  is  therefore  carried 
down  with  it,  lighting  it  up  throughout  its  whole  extent.     To 
produce  the  best  effect  the  vessel  should  be  set  high  enough  to 
give  a  jet  of  considerable  length. 

4.  (page  116.)  M.  Plateau  gives  the  following  directions  for 
preparing  the  liquid  for  these  soap-bubbles  :   i.  Dissolve  one 
part  by  weight  of  white  soap,  cut  into  thin  slices,  in  forty  parts 


37  APPENDIX. 

of  distilled  water,  and  filter.  2.  Mix  two  parts  by  measure  of 
pure  glycerine  with  one  part  of  the  filtered  solution,  in  a  tem- 
perature of  66°  F.,  and,  after  shaking  them  together  long  and 
violently,  leave  them  at  rest  for  some  days.  A  clear  liquid  will 
settle,  with  a  turbid  one  above.  The  lower  is  to  be  sucked  out 
from  beneath  the  upper  with  a  siphon,  taking  the  utmost  care 
not  to  carry  down  any  of  the  latter  to  mix  with  the  clear  liquid. 
A  bubble  blown  with  this  will  last  several  hours  in  the  open 
air.  Or,  the  mixed  liquid,  after  standing  twenty-four  hours, 
may  be  filtered. 

5.  (page  126.)  The  simplest  and  most  satisfactory  way  of  see- 
ing diffraction  fringes  is  to  place  wire  gauze  of  various  coarse- 
ness over  the  object-glass  of  an  ordinary  telescope,  and  then 
to  look  at  some  brilliant  point  of  light,  as  a  star,  or  the  image  of 
the  sun  reflected  from  a  flask  filled  with  water.     The  fringes 
will  vary  with  the  coarseness  of  the  gauze  used.     They  may  be 
seen  even  when  the  meshes  are  a  quarter  of  an  inch  across. 
The  experiment  is  very  easy  and  is  well  worth  trying. 

6.  (page  195.)  The  laws  of  the  reflection  and  refraction  of 
luminous  and  obscure  heat  are  best  illustrated  with  the  lime 
light  and  the  iodine  cell.     Let  the  light  pass  through  the  largest 
aperture  of  the  diaphragm,  and  concentrate  it  by  a  lens.     Let 
the  pencil  thus  concentrated  fall  upon  the  small  mirror  placed 
so  near  that  it  is  not  brought  to  a  focus  till  after  reflection. 
Place  the  blackened  bulb  of  a  differential  thermometer  at  this 
focus,  and  the  reflection  of  the  luminous  heat  is  proved.     Place 
the  iodine  cell  behind  the  lens  so  as  to  cut  off  all  luminous  radi- 
ation, and  again  place  the  bulb  of  the  thermometer  at  the  focus 
previously  marked,  and  the  reflection  of  the  obscure  heat  is 
proved.     For  refraction,  use  the  refracting  prism  instead  of  the 
mirror,  placed  so  near  that  the  light  is  not  brought  to  a  focus 
till  after  refraction.     Of  course  it  is  easy  to  form  invisible  foci 
with  any  lens  or  concave  mirror.     These    experiments  are  in 
every  way  satisfactory.     Care  must  be  taken  in  using  the  iodine 
solution,  as  it  is  very  inflammable.     After  use  it  should  be  re- 
moved from  the  cell  and  kept  in  a  well-corked  bottle. 


APPENDIX.  379 

7.  (page  271.)  The  zinc  used  for  battery  purposes  should  in 
all  cases  be  amalgamated.     This  may  be  done  either  by  im- 
mersing the  zinc  in  mercury,  or  by  rubbing  its  surface  with  that 
vnetal.     In  either  case  the  zinc   should  first  be   cleaned  with 
dilute  sulphuric  acid. 

It  is  well  to  amalgamate  the  zinc  plates  of  a  battery  every 
time  it  is  used,  and  the  best  time  for  doing  this  is  when  the 
battery  is  taken  down  after  being  used,  as  the  zincs  then  need 
no  cleaning.  For  amalgamating  the  zincs  of  a  large  Bunsen's 
battery,  a  cylindrical  vessel  of  soapstone,  made  with  a  core  and 
just  large  enough  for  immersing  the  zincs  in  the  mercury,  will 
be  found  convenient.  With  such  a  vessel,  not  more  than  forty 
pounds  of  mercury  will  be  needed.  After  immersion  in  the 
mercury  the  zincs  should  be  set  to  drain  in  an  iron  sink,  the 
surplus  mercury  being  caught  in  a  vessel  below. 

8.  (page  300.)  Here,  as  elsewhere,  we   have   described  only 
one  or  two  experiments,  which  serve  to  illustrate  the  principles. 
If  the  teacher  has  the  apparatus  for  a  larger  number  of  experi- 
ments, he  will  of  course  make  use  of  it  at  the  proper  point ;  if 
he  has  not,  it  is  hardly  worth  while  that  the  pupil  should  learn 
descriptions  of  experiments  which  he  never  witnesses. 

A  very  pleasing  illustration  of  the  electric  light  in  rarefied  air 
is  afforded  by  the  "  guinea  and  feather  tube  "  used  in  pneumatic 
experiments.  If  the  ends  of  the  tube  are  connected  with  the 
poles  of  the  inductorium  (or  with  the  electrical  machine)  purple 
flashes  of  auroral  light  mark  the  passage  of  the  current  through 
the  tube  when  the  air  is  exhausted.  In  all  experiments  of  this 
kind,  the  room  should  be  darkened. 

Gassiofs  cascade  is  a  simple  and  inexpensive  piece  of  appara- 
tus for  showing  the  electric  light  in  a  vacuum.  It  consists  of  a 
large  glass  goblet  (uranium  glass  is  best),  the  inside  of  which  is 
coated  nearly  to  the  top  with  tinfoil.  Place  the  vessel  on  the 
plate  of  the  air-pump,  cover  it  with  a  receiver  which  has  a  slid- 
ing rod  through  the  top,  bring  the  sliding  rod  in  contact  with 
the  tinfoil  coating,  and  connect  one  pole  of  the  inductorium  (or 
one  conductor  of  the  electrical  machine)  with  the  rod,  and  the 
other  with  the  pump-plate.  When  the  air  is  exhausted,  and 
the  current  sent  through  the  receiver,  streams  of  blue  light  flow 


380  APPENDIX. 

from  the  tinfoil  over  the  side  of  the  vessel  to  the  pump-plate. 
A  variety  of  beautiful  effects  are  produced  by  different  degrees 
of  exhaustion,  and  by  changing  the  direction  of  the  current. 

The  apparatus  known  as  the  Abb£  Nolle  fs  Globe  also  fur- 
nishes very  pretty  displays  of  the  electric  light  in  rarefied  air. 
It  consists  of  a  glass  globe  suspended  in  the  upper  part  of  a 
glass  bell-jar,  and  arranged  so  that  it  can  be  partially  filled  with 
water,  and  connected  with  the  inductorium  or  the  electrical 
machine  by  means  of  a  chain  dipping  into  the  water.  The  light 
in  this  case  flows  in  lambent  streams  from  the  globe  to  the 
pump-plate. 

A  variety  of  pieces  of  apparatus  for  showing  the  electric  light 
are  made  by  pasting  bits  of  tinfoil  about  ^  of  an  inch  apart  on 
glass,  oiled  silk,  or  other  non-conducting  substance.  Letters, 
outline  figures,  etc.,  may  thus  be  formed,  which  appear  in  lines 
of  scintillating  light  when  the  current  is  sent  through  them. 

The  pieces  of  tinfoil  may  be  pasted  in  a  spiral  on  the  inside 
of  a  long  glass  tube,  and  lighted  up  in  the  same  way. 

The  diamond  jar,  as  it  is  sometimes  called,  is  a  Leyden  jar, 
the  coatings  of  which  are  composed  of  small  pieces  of  tinfoil, 
separated  from  one  another.  Brilliant  sparks  pass  between 
these  pieces  when  the  jar  is  charged  or  discharged. 

If  the  knob  of  a  common  Leyden  jar  is  connected  with  one 
pole  of  the  inductorium,  and  a  wire  from  the  other  pole  is 
brought  near  the  outer  coating  of  the  jar,  bright  sparks  pass  in 
most  rapid  succession  between  the  pole  and  the  jar.  The  elec- 
trical machine  may  be  used  instead  of  the  inductorium  in  this 
experiment,  but  the  effect  is  much  less  striking. 

The  teacher  will  find  many  other  experiments  in  the  works 
on  Electricity  mentioned  in  the  Preface,  especially  in  the  little 
book  of  Ferguson's.  To  those  who  have  Ruhmkorff's  •oil,  we 
commend  a  little  volume  by  Noad,  entitled  "  The  Inductorium," 
(London,  John  Churchill  and  Sons,  1866)  which  describes  3 
large  number  of  beautiful  and  instructive  experiments  with  that 
instrument. 


QUESTIONS    FOR    REVIEW    AND 
EXAMINATION. 


PART    FIRST. 

\.  WHAT  is  true  of  the  parts  of  a  stone  or  a  piece  of  wood  } 
2.  What  are  such  bodies  called  ?  3.  When  is  a  body  called  a 
solid  ?  4.  What  substances  are  called  liquids  ?  3.  Give  an  il- 
lustration. 6.  Show  that  a  vessel  cannot  be  filled  with  water 
until  the  air  is  removed  from  it.  7.  What  are  substances  like 
air  called  ?  8.  How  many  states  of  matter  are  there  ?  9.  What 
are  they  called  ?  10.  Show  that  there  is  a  force  drawing  bodies 
toward  the  earth.  11.  What  is  this  force  called?  12.  What 
is  weight?  13.  Show  that  all  bodies  do  not  have  the  same 
weight.  14.  How  can  we  find  how  much  heavier  one  body  is 
than  another?  15.  Describe  the  spring  balance.  16.  Explain 
how  bodies  may  be  weighed  by  it.  17.  Show  how  we  can  find 
the  weight  of  bodies  by  means  of  a  rod  poised  at  its  centre. 
1 8.  Describe  the  balance.  19.  Show  how  we  can  find  the 
weight  of  a  body  by  means  of  a  rod  poised  at  a  point  near 
one  of  its  ends.  20.  Describe  the  steelyard.  21.  When  a  rod 
is  alike  throughout  its  whole  length,  where  must  it  be  supported 
in  order  to  have  the  force  of  .gravity  acting  upon  one  arm  bal- 
ance that  acting  upon  the  other  ?  22.  When  a  weight  is  hung 
to  one  end  of  the  arm  just  twice  as  heavy  as  that  hung  to  the 
other,  where  must  the  rod  be  supported  in  order  to  have  the 
force  of  gravity  acting  upon  one  arm  just  balance  that  acting 
upon  the  other  ?  23.  What  is  true  of  a  disc  of  wood  when 
supported  at  its  centre  ?  24.  What  is  true  of  the  same  disc 
when  one  side  of  it  is  loaded  with  lead  ?  25.  What  point  may 
be  found  for  every  body  ?  26.  What  is  this  point  called  ? 
27.  Define  the  centre  of  gravity  of  a  body.  28.  Show  that  the 
centre  of  gravity  is  not  always  in  the  body  itself.  29.  What  is 
true  of  the  centre  of  gravity  of  two  balls  connected  by  a  rod  ? 
30.  When  a  loaded  disc  which  is  supported  at  its  centre  is 


382          QUESTIONS    FOR    REVIEW   AND    EXAMINATION. 

placed  in  different  positions,  what  is  true  of  it  ?  31.  When  is  a 
body  said  to  be  in  equilibrium  ?  32.  When,  in  stable  equilib- 
rium ?  33.  When,  in  unstable  equilibrium  ?  34.  When,  in  in- 
different equilibrium  ?  35.  Show  that  the  centre  of  gravity 
seeks  the  lowest  point  it  can  reach.  36.  Illustrate  the  different 
kinds  of  equilibrium  by  means  of  spheres.  37.  What  is  true 
of  the  centre  of  gravity  in  each  kind  of  equilibrium  ?  38.  Show 
that  the  broader  the  base  of  a  body  compared  with  its  height, 
the  greater  the  stability  of  its  equilibrium.  39.  Show  that  a 
body  with  a  broad  base  may  be  in  unstable  equilibrium. 

40.  When    may   a    leaning    body  be   in   stable    equilibrium  ? 

41.  Show  that  a  body  having  a  very  narrow  base  may  be  in 
stable  equilibrium.     42.  Show  how  the  centre  of  gravity  of  a 
body  may  be  found.     43.  How  do  we  know  that  liquids  have 
weight  ?    44.  Are  all  liquids  equally  heavy  ?    45.  Show  that 
liquids  when  acted  upon  by  gravity  press  not  only  downward, 
but  also   upward  and  sideways.     46.  Show  that   the   upward, 
downward,  and  lateral  pressures  are  equal  for  the  same  depth 
of  liquid.     47.  Show   that  these  pressures  increase  with   the 
depth.     48.  Show  that  these  pressures  do  not  depend  at  all 
upon   the  form  or  size  of  the  vessel  which   holds  the  liquid. 
49.  Show  what  takes  place  when  different  vessels  are  connect- 
ed, and  one  of  them  filled  with  a  liquid.    50.  Show  that  a  press- 
ure of  -gL  of  a  pound  upon  a  particle  of  water  in  a  closed  vessel 
causes  every  particle  of  water  at  the  surface  to  exert  an  upward 
pressure  of  -£$  of  a  pound.     51.. Show  that  a  pressure  of  -£$ 
of  a  pound  upon  a  particle  of  water  in  a  closed  vessel  causes 
the  particles  of  different  depths  to  exert  the  same  upward  press- 
ure as  those  at  the  surface.     52.  Show  that  when  any  pressure 
is  brought  to  bear  upon  any  particle  of  a  liquid,  each  particle  is 
made  to  exert  the  same  pressure  upward,  downward,  and  side- 
ways.    53-  What  is  true  when  any  pressure  is  brought  to  bear 
upon  any  particle  of  a  liquid  in  a  closed  vessel  ?     54.  How  by 
means  of  a  liquid  may  a  small  pressure  be  made  to  exert  a  great 
one  ?    55.  Describe  the  hydrostatic  press,  and  explain  its  action. 

56.  What    do    all    natural    collections    of   water    illustrate  ? 

57.  Give  an  example.     58.  Explain  the  formation  of  springs. 
59.  Why  are  Artesian  wells  so  named  ?    60.  Explain  their  ac- 
tion.    61.  What   is   true   of  a  body   when   placed   in   water? 


QUESTIONS    FOR    REVIEW    AND    EXAMINATION.  383 

62.  Show  this.  63.  How  much  is  a  body  buoyed  up  in  water  ? 
64.  Show  this.  65.  When  will  a  body  sink  in  water  ?  66.  When 
float  ?  67.  When  a  body  floats  in  a  liquid,  how  much  of  the 
liquid  does  it  displace  ?  68.  Why  do  iron  ships  float?  69.  When 
is  one  body  said  to  be  more  dense  than  another  ?  70.  What  is 
specific  gravity  ?  71.  What  must  be  known  to  find  the  specific 
gravity  of  a  solid  or  liquid  ?  72.  How  can  we  find  the  weight 
of  a  bulk  of  water  equal  to  that  of  a  solid  ?  73.  Describe  the 
hydrometer  in  Figure  23,  and  show  how  the  specific  gravity 
of  a  liquid  is  found  by  means  of  it.  74.  Describe  the  hydrom- 
eter in  Figure  24,  and  explain  how  it  is  used  in  finding 
the  specific  gravity  of  a  liquid.  75.  Show  that  gases  have 
weight.  76.  How  do  gases  press  ?  77.  Show  that  they 
press  in  this  way.  78.  Tell  what  you  can  about  the  hand-glass. 
79.  About  the  Magdeburg  hemispheres.  80.  About  the  weight- 
lifter.  81.  Show  that  gases  have  an  expansive  force.  82.  De- 
scribe the  air-pump,  and  explain  its  action.  83.  Show  that  a 
body  is  buoyed  up  in  the  air.  84.  When  will  a  body  rise  in  the 
air  ?  85.  When  will  it  sink  in  the  air  ?  86.  Why  do  balloons 
rise  ?  87.  With  what  must  they  be  filled  ?  88.  How  are  paper 
balloons  sometimes  made  to  rise  ?  89.  Show  that  the  atmos- 
pheric pressure  will  hold  up  a  column  of  liquid  in  an  inverted 
vessel.  90.  How  high  a  column  of  mercury  will  the  atmos- 
pheric pressure  hold  up  in  a  tube  ?  91.  Show  this.  92.  The 
atmospheric  pressure  is  equal  to  how  many  pounds  to  the 
square  inch  ?  93.  Show  this.  94.  Show  what  is  true  of  the 
atmospheric  pressure  from  day  to  day.  95.  Show  what  is  true 
of  the  atmospheric  pressure  as  we  go  away  from  the  earth. 
96.  Describe  the  barometer.  97.  Give  an  account  of  its  uses. 
98.  How  high  a  column  of  water  will  the  pressure  of  the  atmos- 
phere sustain  ?  99.  How  do  we  know  ?  100.  What  is  a  pump  ? 
101.  Describe  the  lifting  pump,  and  explain  its  action.  102.  De- 
scribe the  force-pump.  103.  What  pumps  are  there  in  the  fire- 
engine  ?  104.  What  is  a  siphon  ?  105.  Explain  the  action  of 
a  siphon.  106.  Explain  Tantalus's  Cup.  107.  Explain  inter- 
mittent springs.  108.  What  increases  the  expansive  force  of 
gases?  109.  Explain  the  air-gun.  110.  Describe  the  conden- 
ser, in.  State  Mariotte's  law.  112.  Illustrate  this  law. 
113.  What  is  a  manometer?  114.  Describe  a  manometer. 


384         QUESTIONS    FOR    REVIEW  AND    EXAMINATION. 

115.  Describe  the  spirit-level,  and  explain  its  use.  116.  Sho\? 
that  gravity  may  put  a  body  in  motion,  as  well  as  cause  it  to 
exert  pressure.  117.  Will  a  body  begin  to  move  or  come  to 
rest  of  itself?  118.  State  the  first  law  of  motion.  119.  How 
do  we  know  that  a  body  will  move  in  this  way?  120.  Show 
that  an  unbalanced  force  must  act  upon  a  body  in  order  to  put 
it  in  motion.  121.  What  is  necessary  to  change  the  speed  or 
direction  of  a  moving  body?  122.  Why  does  it  seem  to  us 
more  natural  for  a  body  to  be  at  rest  than  in  motion? 
123.  What  is  the  effect  of  a  force  acting  upon  a  body  for  a 
moment  only  ?  124.  What  is  the  effect  of  a  force  acting  upon 
a  body  continuously?  125.  Show  that  the  resistance  a  body 
meets  increases  as  the  square  of  its  velocity.  126.  Show  that 
a  moving  body  may  be  in  equilibrium.  127.  State  the  second 
law  of  motion.  128.  Illustrate  this  law  in  the  case  of  a  body 
thrown  forward.  129.  In  the  case  of  a  body  thrown  upward. 
130.  In  the  case  of  a  body  thrown  downward.  131.  When 
does  a  moving  body  acted  upon  by  gravity  describe  a  curved 
path  ?  132.  Illustrate  this.  133.  What  is  true  of  the  speed 
with  which  all  bodies  would  fall  were  it  not  for  the  air? 
134.  Show  that  this  is  so.  135.  At  what  rate  does  gravity 
increase  the  speed  of  a  body  falling  directly  downward  ? 
136.  Show  that  this  is  so.  137.  Show  how  we  find  the  dis- 
tance a  body  falls  in  a  given  time.  138.  Show  at  what  rate 
gravity  retards  the  velocity  of  a  body  moving  directly  upward. 
139.  Show  how  we  find  the  distance  a  body  rises  in  a  given 
time.  140.  What  is  true  of  the  velocity  a  body  always  acquires 
in  falling  the  same  distance  ?  141.  Show  that  this  is  so. 
142.  Through  what  distance  must  a  body  fall,  in  order  to  double 
its  velocity?  143.  With  how  many  times  greater  velocity  must 
a  body  start,  in  order  to  rise  to  double  the  height  ?  144^  How 
does  the  velocity  which  a  falling  body  acquires  compare  with 
the  height  from  which  it  falls.  145.  How  does  the  height  to 
which  a  body  will  rise  compare  with  the  velocity  with  which  it 
starts  ?  146.  Show  that  the  same  force  acting  upon  different 
quantities  of  matter  does  not  impart  to  them  the  same  velocity. 
147.  What  do  we  mean  by  the  mass  of  a  body  ?  148.  By  its 
momentum  ?  149.  Does  the  same  force  always  give  the  same 
momentum  t<?  a  body,  whether  it  be  ^reat  or  small  ?  150.  State 


QUESTIONS    FOR    REVIEW   AND    EXAMINATION.          385 

the  third  law  of  motion,  or  the  law   of  action  and  reaction. 

151.  Illustrate   this   law  by   means   of  lead   and   ivory  balls. 

152.  From  what  does  this  law  result?     153.  What  is  usually 
said  of  a  force  which  acts  in  opposite  directions  ?     154.  Give 
some  illustration  of  this.     155.  Give  some  illustration  of  the 
fact  that  it  requires  time  to  transmit  motion  from  particle  to 
particle  of  a  body.     156.  What  are  the  two  effects  when  a  body 
is  met  by  a  body  in  motion  ?     157.-  How  does  the  power  of  a 
body  to  pierce  another  increase  ?     158.  Give  an  illustration  of 
reflected  motion.     159.  Show  what  is  meant  by  the  angle  of  in^ 
cidence  and  that  of  reflection.     160.  State  the  law  of  reflected 
motion.     161.  What  is  a  pendulum  ?     162.  Explain  the  vibra- 
tion of  a  pendulum.     163.  How  many  kinds  of  pendulum  are 
there  ?    164.  Illustrate  the  first  law  of  the  pendulum.   165.  State 
this   law.     166.  Illustrate   the   second   law  of  the  pendulum. 
167.  State  this  law.     168.  Illustrate  the  third  law  of  the  pen- 
dulum.     169.  State   this   law.      170.  State   and  illustrate   the 
fourth  law  of  the   pendulum.      171.  Describe   the   compound 
pendulum.     172.  Show  how  the  particles  of  a  compound  pen- 
dulum affect  one  another's  movements  ?     173.  What  is  the  cen- 
tre of  vibration  of  a  compound  pendulum  ?     174.  What  is  the 
virtual  length  of  a  compound  pendulum  ?     175.  Show  what  is 
true  of  the  centres  of  vibration  and  of  suspension  ?     176.  What 
is  a  common  clock  ?     177.  Describe  the  action  of  the  escape- 
ment.    178.  To  what  is  the  second-hand  of  a  clock  attached  ? 
179.  What  carries  the  minute-hand  ?    180.  What  carries   the 
hour-hand?     1 8 1.  What  puts  the  clock  in  motion  ?     182.  What 
regulates  the  motion  of  the  clock  ?     183.  How  is  the  pendulum 
kept  vibrating  ?      184.    Show   how  the  pendulum  is  used  for 
measuring  the  force  of  gravity.     185.  Explain  how  a  workman 
raises  a  heavy  stone.     186.  What  is  the  bar  he  uses  called? 
187.  What  is  the  stone  to  be  raised  called  ?     188.  What  is  the 
moving  force  applied  to  the  end  of  the  bar  called  ?     189.  What 
is  the  block  upon  which  the  bar  rests  called  ?     190.  Give  an 
illustration  of  a  lever  in  which  the  power  is  applied  between 
the  weight  and  fulcrum.     191.  How  many  kinds  of  lever  are 
there  ?     192.  In  what  respect  do  they  differ  ?     193.  State  the 
law    of    the    lever,   and   show    its    truth   by   an    illustration. 
194.    What  is   the   law  of  every   machine,    however  compli- 


386          QUESTIONS    FOR   REVIEW    AND    EXAMINATION. 

cated  ?  195.  When  is  there  said  to  be  a  gain  of  power  in  a 
machine?  196.  When,  a  loss  of  power  ?  197.  When  there  is 
again  in  power,  there  is  always  a  loss  in  what  ?  198.  When 
there  is  loss  in  power,  there  is  always  gain  in  what?  199.  What 
is  true  of  the  gain  or  loss  of  power  in  a  lever  of  the  first  kind  ? 
200.  In  a  lever  of  the  second  kind?  201.  In  a  lever  of  the 
third  kind  ?  202.  Explain  the  compound  lever  shown  in 
Figure  54.  203.  Give  an  illustration  of  a  bent  lever.  204.  What 
are  the  lengths  of  the  arms  of  a  bent  lever  ?  205.  Why  cannot 
a  lever  be  conveniently  used  when  a  weight  is  to  be  raised  a 
considerable  distance  ?  206.  Describe  the  rack  and  pinion. 

207.  How  does   the   rack  and   pinion  answer  to  the   lever  ? 

208.  Describe  the  windlass.     209.  How  does  this  differ  from 
the  rack  and  pinion  ?     210.  How  may  the  gain  of  power  in  the 
windlass  be  increased  ?     211.  Describe  the  capstan.     212.  How 
may  the  windlass  be  converted  into  a  wheel  and  axle  ?  213.  How 
may  the  power  be  applied  to  the  wheel?     214.  How  may  the 
law  of  machines  be  illustrated  by  means  of  the  wheel  and  axle  ? 
215.  Describe  the  ratchet.     216.  Why  may  not  the  power  of  a 
wheel  and  axle  be  increased  to  any  extent  ?     217.  Show  how 
several  wheels  may  be  combined  so  as  to  increase  the  power 
of  this  machine?     218.  What  are  cog  wheels?     219.  Explain 
the  gain  of  power   in   the  wheel-work   shown   in  Figure   60. 
220.  What  are  spur-wheels  ?     221.  Crown-wheels  ?     222.  Bevel- 
wheels  ?     223.  What  are  belted  wheels  ?     224.  What  are  some 
of  the  advantages  of  belted  wheels  over  cog  wheels  ?   225.  Show 
how  the  direction  of  the  power  may  be  changed  by  means  of  a 
rope.     226.  What  is  a  pulley  ?     227.  What  is  a  fixed  pulley  ? 
228.  What  is  a  movable  pulley  ?     229.  State  the  law  of  the  pul- 
ley.    230.  Apply  this  law  to  the  systems  of  pulleys  with  one 
rope  shown  in  Figures  65  and  66,  and  show  what  weight  will 
be  balanced  by  a  power  of  one  pound  in  each  case.     231.  Ap- 
ply the  same  law  to  the  system  of  pulleys  with  more  than  one 
rope,  shown  in  Figures  67  and  68,  and  show  what  weight  will 
be  balanced  by  a  power  of  one  pound  in  each  case.     232.  Give 
an  illustration  of  an  inclined  plane.     233.  What  is  the  height 
of  an  inclined  plane  ?     234.  What  is  the  length  of  an  inclined 
plane  ?     235.  Show  that  the  law  of  the  inclined  plane  is  the 
same   as   that  of  other  machines.     236.  What   is   a   weclge  ? 


QUESTIONS    FOR    REVIEW   AND    EXAMINATION.          387 

237.  What  are  its  chief  uses  ?  238.  What  is  a  screw  ?  239.  What 
is  the  nut  ?  240.  What  is  the  inclined  surface  of  the  screw 
called  ?  241.  Show  how  the  mechanical  advantage  of  the  screw 
may  be  increased.  242.  Describe  Hunter's  Screw,  and  explain 
its  action.  243.  Describe  the  endless  screw.  244.  What  is  the 
first  source  of  mechanical  power  mentioned  ?  245.  What  are 
hand  machines  ?  246.  Give  some  illustration  of  hand  ma- 
chines. 247.  Describe  the  crab.  248.  Describe  the  derrick. 
249.  What  is  the  second  source  of  mechanical  power  men- 
tioned ?  250.  What  are  horse-powers?  251.  Show  how  a 
horse  may  be  made  to  raise  weights  by  means  of  pulleys. 

252.  How   can   a  horse  be  made  to  turn   an   upright   shaft  ? 

253.  Show  how  a  horse  may  be  made  to  move  an  endless  plat- 
form, and  thus  to  work  machinery.     254.  By  what  power  are 
ships  sometimes  driven  ?   255.  Describe  a  windmill.   256.  What 
is  true  of  water  as  a  source  of  mechanical  power  ?     257.  What 
is  a  water  wheel  ?     258.  When  are  water  wheels  called  vertical, 
and  when  horizontal  wheels  ?     259.  Describe  the  breast-wheel, 
260.  The  overshot  wheel.     261.  The  undershot  wheel.   262.  De- 
scribe Barker's  mill,  and  explain  its  action.     263.  What  form 
of  the  arms  is  found  to  give  the  greatest  power  to  Barker's 
mill  ?     264.  Why  ?     265.  What  would  be  the  effect  of  increas- 
ing the  number  of  the  arms  in  this  machine  ?     266.  Describe 
the  turbine  wheel.     267.  Describe  Marcet's  globe.     268.  What 
is  shown  by  means  of  this  globe  ?     269.  How  ?     270.  What  is 
a  steam  engine  ?     271.  Show  how  the  elastic  force  of  steam  can 
be  made  to  work  a  piston.     272.  Show  how  the  motion  of  the 
piston-rod  may  be  made  to  turn  a  crank.     273.  Describe  the 
engine  shown  in  Figure  89.     274.  Explain  the  action  and  use 
of   the   governor.      275.    Explain   the   use   of   the   fly-wheel. 
276.  Explain  the  difference  between  a  high  and  a  low  pressure 
engine.      277.    What   must  the   boiler  be   capable   of  doing? 
278.  Of  what   are   boilers   usually  made  ?     279.  Describe  the 
Cornish   boiler.     280.  Describe  the  boiler  shown  in    Figures 
91  and  92.     281.  Describe  the  boiler  of  a  locomotive  engine. 
282.  Describe  the  locomotive  engine. 


QUESTIONS    FOR    REVIEW    AND 
EXAMINATION. 


PART    SECOND. 
SOUND. 

i.  What  is  the  condition  of  a  sounding  body?  2.  Show  this. 
3.  Can  sound  traverse  a  vacuum  ?  4.  Show  this.  5.  Can  sound 
pass  through  gases  ?  6.  Show  this.  7.  Can  it  pass  through 
solids  and  liquids  ?  8.  Show  this.  9.  How  is  sound  propa- 
gated ?  10.  Explain  this  propagation.  11.  Upon  what  does 
the  intensity  of  sound  depend?  12.  Show  this.  13.  At  what 
rate  does  the  intensity  of  the  sound  diminish  with  the  distance  ? 
14.  Illustrate  this.  15.  Explain  the  use  of  speaking-tubes. 
1 6.  What  is  the  velocity  of  sound  in  air?  17.  Explain  how  this 
velocity)  was  found.  18.  What  is  the  computed  velocity  of 
sound  i$Aair  ?  19.  Explain  the  disagreement  between  this  and 
the  observed  velocity.  20.  Upon  what  does  the  velocity  of 
sound  in  any  medium  depend  ?  21.  Does  the  velocity  of  sound 
vary  with  the  elevation  of  the  place  ?  22.  Why  is  this  so  ? 
23.  What  is  the  velocity  of  sound  in  water  ?  24.  How  was  this 
found  ?  25.  How  does  the  velocity  of  sound  in  air  compare 
with  its  velocity  in  solids  ?  26.  Illustrate,  by  means  of  ivory 
balls,  the  transmission  of  the  vibration  of  sound  from  particle 
to  particle,  and  show  what  takes  place  when  the  sound-wave 
meets  a  new  medium.  27.  What  is  true  of  the  angles  of  inci- 
dence and  reflection  ?  28.  Show  this.  29.  Explain  echoes. 
30.  Give  an  account  of  some  remarkable  echoes.  31.  What 
takes  place  when  a  sound-wave  passes  obliquely  mto  a  new 
medium  ?  32.  Explain  this  fully,  and  give  an  illustration. 
33.  What  is  the  difference  between  a  musical  sound  and  a 
noise  ?  34.  Give  an  illustration  of  a  musical  sound,  and  show 
upon  what  its  pitch  depends.  35.  Describe  the  tuning-fork. 
36.  Describe  the  siren.  37.  Explain  how  the  rate  of  a  body's 
vibration  may  be  found.  38.  Show  how  to  find  the  length  of  a 


QUESTIONS    FOR    REVIEW    AND    EXAMINATION.          389 

sound-wave.  39.  When  do  sounds  differ  by  an  octave  ? 
40.  Describe  the  sonometer.  41.  What  effect  has  the  length  of 
a  string  upon  the  rapidity  of  its  vibration?  42.  Show  this. 

43.  Illustrate  the  formation  of  nodes  by  means  of  the  sonometer. 

44.  Show    that    nodes    may    be   formed    in   vibrating  plates. 

45.  What  is  meant  by  the  fundamental  tone  of  a  body  ?    46.  By 
its  overtones  or  harmonics  ?    47.  To  what  is  the  quality  of  sound 
due  ?    48.  What  does  Tyndall  propose  to  call  the  quality  of 
sound  ?      49.    Show   that  musical  sounds  can  be  transmitted 
through  liquids.     50.  Give  Tyndall's  illustration  of  the  trans- 
mission of  musical  sounds  through  solids.     51.  Wheatstone's 
illustration  of  the  same.     52.  What  are  sympathetic  vibrations  ? 

53.  Illustrate   these   vibrations   by   means   of  the   sonometer. 

54.  By  means  of  tuning-forks.    55.  By  means  of  clocks.    56.  De- 
scribe the  super-position  of  water-waves.     57.  What  is  the  law 
of  this  mingling  of  the  waves  ?     58.  Show  that  a  great  variety 
of  sound-waves  may  traverse  the  air  together.     59.  When  are 
sound-waves  said  to  interfere  ?   60.  Illustrate  this  interference  by 
means  of  a  long  bent  tube.     61.  By  means  of  a  vibrating  plate. 
62.  By  means  of  a  tuning-fork.     63  What  are  beats  ?    64.  Illus- 
trate their  formation  by  means  of  tuning-forks.     65.  TO  what  is 
their  number  per  second  equal  ?     66.  Illustrate  beats  by  means 
of  organ-pipes.     67.  By  means  of  sounding  flames.     68.  Give 
Tyndall's  illustration  of  resultant   tones.     69.  Illustrate  these 
tones  by  means  of  the  siren,  and  show  to  what  rate  of  vibration 
their  pitch  answers.     70.  What  was   Young's   explanation   of 
resultant  tones  ?     71.  Why  is  this  explanation  unsatisfactory? 
72.   Give    Helmholtz's  explanation.     73.  What  are   difference 
tones   and    summation    tones  ?      74.   When   are   two   musical 
sounds   in   unison  ?      75.    When    do    they    form   an    octave  ? 
76.  When  a  fifth  ?     77.  When  a  fourth  ?     78.  When  a  major 
third  ?      79.  When   a   minor  third  ?     80.   What  is   a   chord  ? 
81.  What  is  a  discord  ?     82.    Which  chords  are  most  agree- 
able ?     83.  Give  Euler's  explanation  of  chords  and   discords. 
84.    State    the    objections    to    this     explanation.       85.    Give 
Tyndall's   illustration   of  Helmholtz's   explanation   of  discord. 
86.    State    Helmholtz's   theory.     87.    Are   those  combinations 
of   notes    which    are     actually    found    to    be    agreeable    and 
disagreeable    fully    explained    by    this    theory  ?      88.     Show 


3QO         QUESTIONS    FOR   REVIEW   AND    EXAMINATION. 

this.  89.  Give  an  account  of  the  musical  scale.  90.  What 
are  stringed  instruments?  91.  Show  that  a  string  vibrating 
alone  gives  only  a  feeble  sound.  92.  Illustrate  the  use  of  a 
sounding-board.  93.  State  the  laws  of  the  vibration  of  strings, 
and  illustrate  each.  94.  Illustrate  the  longitudinal  vibration 
of  a  wire.  95.  Show  that  the  longitudinal  vibration  of  a  wire 
grows  more  rapid  as  the  wire  is  shortened.  96.  Show  that  the 
rapidity  of  these  vibrations  is  independent  of  the  tension  of  the 
wire.  97.  Show  how  to  find  the  relative  velocity  of  sound  in 
wires  of  different  material.  98.  Give  an  account  of  the  longi- 
tudinal vibration  of  rods  free  at  one  end.  99.  Illustrate  the 
longitudinal  vibration  of  a  rod  free  at  both  ends.  100.  Illus- 
trate the  lengthening  and  shortening  of  the  halves  of  such  a 
rod.  101.  Show  how  to  find  the  relative  velocity  of  sound  in 
different  solids.  102.  Illustrate  resonance.  103.  What  is  the 
length  of  a  column  of  air  which  resounds  to  any  tuning-fork  ? 
104.  Show  this.  105.  Explain  resonance.  106.  Give  Savart's 
illustration  of  resonance.  107.  Give  some  further  illustrations 
of  resonance.  108.  Show  that  a  column  of  air  in  a  tube  has 
power  to  select  and  reinforce  particular  sounds.  109.  Explain 
what  takes  place  on  blowing  across  the  mouth  of  a  tube. 
I  ib.  Show  at  what  rate  the  vibration  of  a  column  of  air  in  a  tube 
varies  with  its  length.  in.  What  are  stopped  and  what 
open  tubes  ?  112.  How  do  the  notes  given  by  a  stopped  and 
by  an  open  tube  compare?  113.  What  are  organ-pipes? 
1 14.  Explain  how  they  are  made  to  speak.  115.  Show  how  the 
condition  of  the  air  within  an  open  pipe  may  be  examined  by 
means  of  a  stretched  membrane.  116.  What  is  the  condition 
of  this  air  found  to  be?  117.  Show  how  the  condition  of  the 
air  inside  an  organ-pipe  may  be  examined  by  means  of  gas-jets. 
1 1 8.  Why  does  an  open  pipe  give  the  octave  of  a  closed  pipe 
of  the  same  length?  119.  Show  how  to  find  the  relative  ve- 
locity of  sound  in  different  gases.  120.  In  different  liquids. 
121.  Show  how  to  find  the  real  velocity  of  sound  indifferent 
substances.  122.  What  are  reed  pipes  ?  123.  Explain  the 
action  of  the  reed.  124.  When  is  the  sound  of  the  reed  pipe 
most  pure  and  forcible  ?  125.  Illustrate  the  action  of  a  reed  by 
means  of  a  straw.  126.  Give  some  illustrations  of  reed  instru- 
ments. 127.  What  are  the  two  classes  of  wind  instruments? 


QUESTIONS    FOR    REVIEW   AND    EXAMINATION.          391 

128.  What  is  always  true  of  friction  ?  129.  Give  some  illus- 
trations. 130.  How  may  the  noise  of  a  gas-flame  be  converted 
into  a  musical  note  ?  131.  Show  upon  what  the  pitch  of  a 
sounding  flame  depends.  132.  Show  that  a  sounding  flame  is 
alternately  extinguished  and  relighted.  133.  Does  the  pitch  of 
a  sounding  flame  depend  at  all  upon  the  size  of  the  flame  ? 
134.  Show  this.  135.  Give  some  account  of  sensitive  flames 
within  tubes.  136.  Describe  the  organs  of  the  human  voice, 
and  illustrate  their  action.  137.  Explain  the  formation  of  vowel 
sounds.  138.  Describe  the  human  ear.  139.  Give  an  account 
of  the  range  of  the  human  ear. 


LIGHT. 

140.  Define  a  luminous  and  a  non-luminous  body.  141. 
Show  that  a  luminous  body  sends  out  light  in  every  direction. 
142.  Define  transparent  and  opaque  bodies.  143.  Show  that 
light  traverses  space  in  straight  lines,  and  explain  the  forma- 
tion of  shadows.  144.  Define  a  ray,  a  pencil,  and  a  beam  of 
light.  145.  Find  the  velocity  of  light.  146.  At  what  rate  does 
the  intensity  of  light  diminish  with  the  distance  ?  Show  this. 
147.  What  is  a  photometer  ?  148.  Describe  Count  Rumford's 
photometer.  149.  What  happens  when  light  meets  a  new 
medium  ?  Illustrate.  150.  State  and  illustrate  the  law  of  re- 
flection. 151.  Upon  what  does  the  intensity  of  reflected  light 
depend?  Illustrate.  152.  When  is  light  said  to  be  diffused? 
153.  State  and  illustrate  the  law  of  refraction.  154.  What  is 
the  index  of  refraction  ?  155.  Explain  total  reflection.  156. 
Explain  mirage.  157.  Mention  and  explain  other  effects  of 
refraction.  158.  Show  the  path  of  the  rays  through  a  medium 
with  parallel  faces.  159.  Through  a  prism.  160.  Illustrate  dis- 
persion. 161.  Explain  the  achromatic  prism.  162.'  Show  that 
the  prismatic  colors  are  simple  and  unequally  refrangible.  163. 
Illustrate  the  composition  of  white  light.  164.  What  three 
colors  will  produce  white  light  by  their  mixture  ?  165.  Why 
cannot  the  spectrum  be  made  up  of  red,  yellow,  and  blue  ? 
166.  When  are  calors  said  to  be  complementary  ?  167.  Illus- 
trate absorption.  168.  Explain  the  color  of  bodies.  169.  Show 


392         QUESTIONS    FOR    REVIEW   AND    EXAMINATION. 

how  to  analyze  the  color  of  bodies.  170.  Show  that  different 
substances  give  flames  of  different  colors.  171.  Describe  the 
spectroscope,  and  explain  its  use.  172.  Show  that  gases  ab- 
sorb the  same  kind  of  light  that  they  emit  when  incandescent. 
173.  What  are  Fraunhofer's  lines  ?  174.  Account  for  their 
presence  in  the  spectrum  of  sunlight  and  starlight.  175.  De- 
scribe the  colors  of  the  soap-bubble.  176.  Show  that  these 
colors  are  independent  of  the  liquid  of  which  the  bubble  is 
made.  177.  Show  to  what  these  colors  are  due.  178.  Why 
do  we  suppose  that  light  is  transmitted  by  vibrations?  179. 
Why  is  the  bubble  black  at  the  top  just  before  it  bursts  ?  180. 
Illustrate  the  change  of  the  phase  of  the  wave  when  reflected 
from  the  surface  of  a  rarer  medium.  181.  Find  the  distance 
between  the  reflecting  surfaces  at  the  different  colored  rings. 
182.  What  is  the  ether?  183.  Find  the  length  of  the  light- 
waves for  the  different  colors.  184.  What  is  the  origin  of 
light  ?  185.  Why  do  different  substances  emit  light  of  different 
colors  ?  1 86.  Why  do  different  substances  absorb  light  of 
different  colors  ?  187.  Illustrate  diffraction  fringes.  188.  Ex- 
plain the  formation  of  these  fringes.  189.  Show  the  action 
of  Iceland  spar  upon  light.  190.  Describe  the  double-refracting 
prism.  191.  Show  that  the  ordinary  and  extraordinary  rays 
are  both  polarized.  192.  Explain  polarization  and  double 
iefraction.  193.  Show  the  action  of  tourmaline  upon  ordinary 
light.  194.  Show  that  light  may  be  polarized  by  reflection  and 
by  refraction.  195.  Define  a  polarizer  and  an  analyzer.  196. 
Describe  a  Nicol's  prism,  and  explain  its  action.  197.  Show 
that  polarized  light  can  interfere  only  when  the  rays  are  polar- 
ized in  the  same  plane.  198.  Explain  circular  and  elliptical 
polarization.  199.  Illustrate  and  explain  rotatory  polarization. 
200.  Explain  the  colors  seen  in  crystalline  plates  by  polarized 
light.  20 1.  Mention  other  phenomena  of  polarized  light.  202. 
Describe  the  tourmaline  pincette.  203.  Explain  the  rainbow. 
204.  Describe  the  different  kinds  of  lenses.  205.  Explain  the 
action  of  the  double-convex  lens.  206.  Explain  the  formation 
of  images  by  lenses.  207.  Describe  the  camera  obscura.  208. 
Describe  the  eye.  209.  Explain  the  adjustment  of  the  eye. 
210.  Describe  the  retina.  211.  Explain  the  action  of  light 
upon  the  optic  nerve.  212.  Show  that  the  sensation  of  light 


QUESTIONS    FOR    REVIEW   AND    EXAMINATION.         393 

may  be  produced  by  other  causes  than  light  itself.  213.  Illus- 
trate the  duration  of  the  impression  of  light  upon  the  retina. 
214.  Describe  and  explain  the  thaumatrope.  215.  What  is 
irradiation  ?  Illustrate.  216.  Show  that  the  sensibility  of  the 
retina  is  easily  exhausted.  217.  What  is  color-blindness  ? 
218.  Explain  single  vision.  219.  Define  optical  axis  and  vis- 
ual angle.  220.  How  do  we  estimate  the  size  of  an  object  ? 
221.  Show  how  we  estimate  the  distance  of  an  object.  222. 
Why  do  near  bodies  appear  solid  ?  223.  Describe  the  stereo- 
scope. 224.  State  and  illustrate  the  laws  of  distinct  vision. 
225.  Describe  the  simple  microscope.  226.  The  compound 
microscope.  227.  The  telescope.  228.  The  terrestrial  tele- 
scope. 229.  The  opera-glass.  230.  The  magic  lantern.  231. 
The  solar  microscope.  232.  Explain  the  action  of  plane  mir- 
rors upon  light.  233.  Explain  the  formation  of  multiple 
images  by  plane  mirrors.  234.  Explain  the  action  of  concave 
mirrors  upon  parallel  and  upon  divergent  rays.  235.  Explain 
the  formation  of  images  by  concave  mirrors.  236.  Explain  the 
action  of  convex  mirrors  upon  parallel  and  divergent  rays.  237. 
Describe  the  reflecting  telescope.  238.  Explain  the  action  of 
parabolic  mirrors.  239.  Illustrate  the  chemical  action  of  light. 
240.  Give  an  account  of  the  daguerreotype  process.  241.  Of 
the  collodion  process.  242.  Of  photographic  printing.  243. 
Show  the  chemical  action  of  the  solar  spectrum. 


HEAT. 

244.  Show  that  heat  is  radiated  in  all  directions.  245.  Show 
that  heat  traverses  space  in  straight  lines,  and  with  the  velocity 
of  light.  246.  Define  luminous  and  obscure  heat.  247.  Define 
diathermancy.  248.  Show  that  heat  is  reflected  in  the  same 
way  as  light.  249.  That  it  is  refracted  like  light.  250.  That  it 
is  dispersed  like  light.  251.  That  heat  and  light  are  one  and 
the  same.  252.  Find  the  proportion  of  obscure  and  luminous 
radiation  in  the  electric  light,  and  in  sunlight.  253.  Show  that 
the  obscure  radiation  increases  in  intensity  with  the  tempera- 
ture. 254.  What  are  invisible  foci,  and  how  may  they  be 
formed?  255.  Explain  calorescence,  fluorescence,  and  phos- 
17* 


394         QUESTIONS    FOR    REVIEW   AND    EXAMINATION. 

phorescence.  256.  Show  that  different  solids  and  liquids  ab- 
sorb the  same  kind  of  heat  differently.  257.  Show  that  the 
same  solid  absorbs  different  kinds  of  heat  differently.  258. 
What  is  meant  by  the  quality  of  heat  ?  259.  Show  that  differ- 
ent gases  absorb  the  same  quality  of  heat  differently.  260. 
Show  that  the  same  gas  absorbs  different  qualities  of  heat 
differently.  261.  Show  that  vapors  absorb  the  same  quality 
of  heat  in  the  same  order  as  their  liquids.  262.  Show  that 
good  absorbers  are  good  radiators.  263.  Show  how  bodies 
radiate  and  absorb  heat.  264.  Show  upon  what  the  absorptive 
power  of  bodies  depends.  265.  What  is  the  condition  of  the 
molecules  of  bodies  ?  266.  Illustrate  conduction.  267.  Show 
that  different  substances  have  different  conducting  powers. 

268.  Show  that  liquids  and  gases  are  poor  conductors  of  heat. 

269.  Show  that  a  body  in  cooling  i°  gives  out  as  much  heat  as 
it  takes  to  warm  it   i°.     270.  Show  that  it  takes  different 
amounts  of  heat  to  raise  the  temperature  of  the  same  weight 
of  different  substances  i°.     271.  Define  a  unit  of  heat.     272. 
Define  specific  heat.     273.  Find  the  specific  heat  of  bodies  by 
the  method  of  mixture.     274.  By  the  method  of  fusion.     275. 
Find  the  specific  heat  of  liquids  and  gases  by  means  of  the 
calorimeter.     276.  Show   that   heat   will   melt  a  solid.      277. 
What  is  meant  by  the  melting-point  ?     278.  Show  that  liquids 
have  latent  heat.     279.  Find  the  latent  heat  of  a  liquid.     280. 
Explain  the  boiling  of  liquids.     281.  Show   that  gases   have 
latent  heat.     282.  Upon  what  does  the  state  of  a  body  depend  ? 
283.  Show  the  effect  of  pressure  upon  the  boiling-point.     284. 
Of  cohesion.     285.  Of  the  nature  of  the  vessel.     286.  Describe 
and  explain  the  spheroidal  state.     287.  Illustrate  evaporation. 
288.  Give  an  account  of  the  condensation  of  gases.     289.  De- 
scribe and  explain  freezing-mixtures.     290.  Show  that  solids 
are  expanded   by  heat.      291.  That  different   solids  are  ex 
panded  differently  by  the  same  heat.      292.  That  liquids  are 
expanded  by  heat.     293.  That  different  liquids  are  expanded 
differently  by  the  same  heat.     294.  That  gases  are  expanded  by 
heat.     295.  That  all  gases  are  expanded  equally  by  the  same 
heat.      296.    Find  the   coefficient    of  expansion   for  mercury. 
297.  For  any  liquid.     298.  For  any  solid.     299.  For  air  ami 
other  gases.     300.  Show  that  when  a  gas  is  not  allowed  to 


QUESTIONS   FOR   REVIEW  AND   EXAMINATION.         39$ 

expand,  its  elasticity  is  increased  by  heat.  301.  Illustrate  the 
convection  of  heat  in  liquids.  302.  How  are  oceanic  currents 
produced  ?  303.  In  gases.  304.  Show  the  effect  of  the  spe- 
cific and  latent  heat  of  water  upon  climate.  305.  Show  the 
effect  of  its  irregular  expansion  and  contraction.  306.  What  is 
true  of  the  latent  heat  of  steam  and  vapor  ?  307.  Explain 
heating  by  steam.  308.  Describe  the  mercurial  thermometer. 
309.  Show  how  it  is  made.  310.  When  and  why  is  an  alcohol 
thermometer  used  ?  311.  Describe  the  air  thermometer.  312. 
The  differential  thermometer.  313.  Breguet's  thermometer. 
314.  Show  the  effect  of  temperature  upon  time-pieces.  315. 
Explain  Graham's  pendulum.  316.  The  compensation  balance- 
wheel.  317.  Mention  other  effects  of  expansion  by  heat.  318. 
Explain  the  dew-point  hygrometer.  319.  The  wet  and  dry  bulb 
hygrometer.  320.  The  hygrodeik. 

ELECTRICITY. 

321.  What  is  the  distinguishing  characteristic  of  a  magnet? 
Illustrate.  322.  Show  that  the  magnetic  force  resides  chiefly 
at  the  ends  of  a  magnet.  323.  Show  that  the  forces  at  the  op- 
posite ends  of  a  magnet  act  in  opposite  directions.  324.  What 
is  meant  by  the  north  and  south  poles  of  a  magnet?  Illustrate. 
325.  What  is  the  effect  on  a  piece  of  soft  iron  of  bringing  it  into 
contact  with  a  magnet  ?  On  a  piece  of  steel  ?  326.  What  is  a 
loadstone  ?  327.  Whence  does  a  magnet  derive  its  name  ? 
328.  Of  what  are  ordinary  magnets  made  ?  329.  What  are 
their  usual  forms  ?  330.  State  what  takes  place  when  a  small 
horizontal  or  dipping  needle  is  moved  alongside  a  bar  magnet. 
331.  Show  that  the  earth  acts  like  a  large  magnet.  332.  What 
is  the  effect  of  like  and  unlike  poles  of  magnets  on  each  other  ? 
333.  What  name  do  the  French  give  to  the  north  pole  of  the 
magnet  ?  Why  ?  334.  How  are  magnets  made  ?  335.  De- 
scribe the  voltaic  pair.  336.  What  is  the  electric  current  ? 
337.  What  is  said  of  its  direction  ?  338.  What  is  a  galvanom- 
eter ?  339.  Describe  the  astatic  needle,  and  the  astatic  gal- 
vanometer. 340.  Describe  and  explain  the  rheostat.  341.  What 
has  been  proved  by  means  of  the  rheostat  ?  342.  Explain 
Ohm's  law.  343.  Explain  quantity  and  intensity.  344.  How 


396          QUESTIONS   FOR   REVIEW  AND   EXAMINATION. 

can  we  increase  the  quantity  of  the  current  ?  the  intensity  ? 
345.  What  is  the  best  material  for  the  active  plate  in  the  vol- 
taic pair  ?  346.  What  is  the  liquid  commonly  used  ?  347. 
What  is  meant  by  local  action  ?  348.  How  may  it  be  pre- 
vented ?  349.  What  effect  is  produced  by  the  adhesion  of  the 
hydrogen  to  the  passive  plate  ?  350.  Describe  Grove's  cell. 
351.  Bunsen's  cell.  352.  DanielFs  cell.  353.  Describe  and 
explain  the  different  ways  of  connecting  the  cells  of  a  battery. 
354.  Define  electrolysis,  electrolyte,  electrode,  anode,  cathode, 
anion,  and  cation.  355.  Explain  in  full  the  electrolysis  of  cupric 
sulphate,  when  the  anode  is  of  platinum.  When  the  anode 
is  of  copper.  356.  Describe  the  voltameter,  and  explain  its 
use.  357.  What  is  an  electro-magnet  ?  358.  What  is  a  helix  ? 

359.  What  is  the  effect  of  reversing  the  current  in  the  helix  ? 

360.  What  is  true  of  the  strength  of  electro-magnets  ?     361. 
Show  that  the  wire  through  which  a  current  passes  is  magnetic. 
362.  How  may  a  current  be  induced  in  a  conductor  by  a  con- 
stant magnet  ?    363.  By  a  variable  magnet  ?    364.  Show  that 
heat  may  be  developed  by  the  current.    365.  To  what  is  the 
heat  developed  proportional  ?     366.    Describe  the  voltaic  arc, 
and  its  luminous  and  thermal  effects.     367.  How  may  we  show 
that  a  current  can  be  developed  by  heat  ?     368.  What  name  is 
given  to  electricity  thus  developed  ?    369.  What  is  a  thermo- 
electric battery  ?    370.  What  is  its  chief  use  ?    371.  Show  that 
electricity  may  be  developed  by  friction.      372.    Describe  the 
electrical  machine.     373.  What  is  true  of  the  quantity  and  of 
the  intensity  of  frictional  electricity  ?     374.  Prove  this.     375. 
How  does  frictional  electricity  compare  with  voltaic  electricity  ? 

376.  Compare  the  electrical  machine  with  the  cell  of  a  battery. 

377.  What  is  an  electroscope  ?     378.  Describe  two  forms  of 
the  instrument,  and  the  action  of  each.     379.  Prove  that  two 
kinds  of  electricity  are  developed  by  the  machine,  and  that 
these  two  forces  act  in  opposite  directions.     380.  What  names 
are  given  to  these  two  kinds  of  electric  force  ?    381.  Can  one 
kind  of  electricity  be  developed  without  at  the  same  time  devel- 
oping the  other  ?    382.  When  is  a  body  said  to  be  polarized  ? 
383.  When  to  be  charged  ?     384.  When  neutral  ?     385.  How 
must  a  polarized  insulated  conductor  be  situated  to  become 
charged  ?    386.  How  to  become  charged  with  the  same  force 


QUESTIONS    FOR   REVIEW  AND   EXAMINATION.         397 

as  that  on  the  polarizing  body  ?  387.  How  to  become  charged 
with  the  opposite  force  ?  388.  Show  that  polarization  of  an  in- 
sulated conductor  depends  upon  the  non-conducting  medium 
which  separates  it  from  the  charged  body.  389.  On  what  part 
of  a  solid  conductor  is  the  charge  always  found  ?  390.  How  is 
the  charge  distributed  over  the  surface  ?  391.  Show  that  po- 
larization rises  highest  in  the  direction  of  least  resistance. 
392.  Show  that  the  charge  which  a  body  can  receive  depends 
upon  the  facilities  it  offers  for  polarization.  393.  Describe  the 
Leyden  jar.  394.  Explain  how  it  is  discharged.  395.  Describe 
the  Leyden  battery.  396.  Explain  the  action  of  points  on 
charged  conductors.  397.  Explain  the  action  of  the  electric 
wheel.  398.  What  is  a  magneto-electric  machine  ?  399.  What 
are  the  chief  peculiarities  of  Wilde's  machine  ?  400.  De- 
scribe the  ordinary  form  of  induction  coil.  401.  What  is  said 
of  Ruhmkorff's  coil?  402.  Describe  Foucault's  self-acting 
rheostat.  403.  What  are  Geissler's  tubes  ?  404.  Describe 
and  explain  the  process  of  electro  typing.  405.  Describe  the 
process  of  electro-plating.  406.  Of  electro-gilding.  407.  What 
two  kinds  of  electro-metallurgy  ?  408.  Show  how  the  electric 
force  may  be  used  to  regulate  the  motion  of  clocks.  409.  What 
four  things  essential  to  an  electric  telegraph  ?  410.  Describe 
the  receiving  instrument  of  Morse's  telegraph.  411.  The  send- 
ing instrument.  412.  Describe  and  explain  the  relay.  413. 
Describe  the  sending  and  receiving  instruments  of  the  Com- 
bination Printing  Telegraph.  414.  Explain  the  electric  fire- 
alarm.  415.  Describe  a  submarine  cable.  416.  What  is  said 
of  electric  lamps  ? 


INDEX. 


[As  Part  First  and  Part  Second  are  paged  separately,  each  has  its  own  Index. ,] 


PART    FIRST. 


Action  and  reaction,  60. 

Air,  buoys  up  bodies,  33. 

elasticity  of  the,  42. 

pressure  of  the,  29. 

diminishes  with  the  height  of  the 

place,  35. 
equal  to  15  pounds  on  a  square 

inch,  35. 
sustains  a  column  of  mercury  30 

inches  high,  34. 
varies  from  day  to  day,  35. 
resists  the  fall  of  bodies,  53. 
Air-gun,  the,  41. 
Air-pump,  the,  31. 
Artesian  wells,  19. 


Balance,  the, 


B. 

'hydrostatic,  21. 
spring,  4. 
Balloons,  33. 
Barker's  mill,  97. 
Barometer,  the,  36. 
Boiler,  the  steam,  105. 
Cornish,  105. 
French,  106. 
locomotive,  108. 
Buoyancy  of  gases,  33. 
liquids,  20. 


Capstan,  the,  79,  92,  94. 
Centre  of  gravity,  6. 

seeks  lowest  point,  8. 
of  a,  solid  found,  n. 
Clocks,  the  construction  of,  68. 
Condenser,  the,  46. 
Cornish  boiler,  the,  105. 
Crab,  the,  92. 
Crank,  the,  77,  78. 

dead  points  1.1  motion  of,  io«. 

used  in  steam  engine,  102. 


D. 


Density  defined,  22. 
Derrick,  the,  92. 


Equilibrium,  8. 

of  moving  bodies,  49. 
stability  of,  9. 


F. 


Falling  bodies,  53,  113. 
Fire-engine,  the,  39. 
Fly-wheel,  the,  104. 
Force-pump,  the,  37. 
French  ste.am  boiler,  the,  106. 

weights  and  measures,  114. 


G. 

buoyancy  of,  33. 
expansive  force  of,  31. 
have  weight,  29. 
pressure  of,  29. 
specific  gravity  of,  45. 
weight  of  bodies  in,  33. 
Governor,  the,  104. 
Gravity,  centre  of,  6. 

solids  found,  n. 
curves  the  path  of  bodies  thrown 

horizontally,  52. 

increases  the  speed  of  falling  bod- 
ies, 53. 
retards  the  speed  of  ascending 

bodies,  54. 

specific,  22  (see  Specific  gravity). 
Gunpowder,  action  of,  41,  60. 

H. 

Hand-glass,  the,  29. 

machines,  92. 

power,  92. 

Hemispheres,  Magdeburg,  30. 
Horse-power,  94. 
Hydrometer,  the,  22. 
Hydrostatic  balance,  the,  21. 
press,  the,  17. 

I. 

Inclined  plane,  the,  85. 

law  of,  86 
Inertia,  4& 


400 


INDEX. 


L. 

Power,  sources  of  mechanical,  92. 
Press,  the  hydrostatic,  17. 

Law,  Mariotte's,  41. 
of  machines,  75. 

Pressure  of  the  air,  34  (see  Air), 
gases,  29  (see  Gases). 

the  lever,  74. 
inclined  plane,  86. 

liquids,  13  (see  Liquids). 
Problems  on  specific  gravity,  27. 

pulley,  83. 

the  pendulum,  71. 

Laws  of  motion,  47  (see  Motion). 

pressure  of  gases,  45. 

Level,  the,  43. 

liquids,  25. 

Lever,  the,  73,  95. 

second  law  of  motion. 

bent,  76. 

55>  371- 

compound,  76. 

simple  machines,  91. 

law  of,  74. 

third  law  of  motion,  64. 

mechanical  advantage  of,  75. 
three  kinds  of,  73. 

Pulley,  the,  83,  92.  93,  94. 
the  law  of,  83. 

Liquids,  3. 

Pumps,  37. 

buoy  up  bodies,  20. 

air,  31. 

how  to  find  the  weight  of,  13. 
press  equally  in  afl  directions, 

force,  37. 
lifting,  37. 

jo    07. 

pressure  of,  not  affected  by  shape 

R. 

of  vessel,  14. 

on  sides  of  vessel,  26 

Rack  and  pinion,  the,  77. 

(foot-note). 

Ratchet,  the,  80. 

transmitted  equally  in 

Reaction,  60. 

all  directions,  15. 

water  wheels,  1  1  1. 

specific  gravity  of,  22,  25. 

Reflected  motion,  62. 

Resistance  to  motion,  49. 

M. 

S. 

Machines,  73. 

law  of,  75. 

Safety-valve,  the,  106. 

Magdeburg  hemispheres,  30. 
Manometer,  the,  48,  100. 

Screw,  the,  87. 
differential,  or  Hunter's,  88. 

Marcet's  globe,  too. 

endless,  89. 

Mariotte's  law,  47. 

Ships,  iron,  21. 

Mass  defined.  58. 

sails  of,  95. 

Matter,  4. 

Siphon,  the,  39. 

acted  upon  by  gravity,  4. 

Solids.  3. 

states  of,  4. 
Measures,  tables  of  French,  370. 
Momentum,  58. 

Specific  gravity,  22. 
of  a  gas,  45. 
liquid,  22,  25. 

Motion,  47. 

solid,  22. 

first  law  of,  47. 
quantity  of,  58. 

Spirit  level,  the,  43. 
Spring  balance,  the,  4. 

reciprocating,  102. 

Springs,  19. 

reflected,  62. 

Steam  engine,  the,  100. 

resistance  to,  49. 

high  and  low  pressure, 

rotary,  102. 

105. 

second  law  of,  50. 

locomotive,  108. 

third  law  of,  58. 

power,  100. 

Steelyard,  the,  5. 

P. 

T. 

Parabola,  motion  in  a,  52. 

Tantalus's  Cup,  40. 

Pendulum,  the,  47,  55,  65. 

V. 

compound,  67. 

laws  of,  65. 

Vacuum  defined,  33. 

reversible,  78. 

Velocity  of  falling  bodies,  53,  55. 

used  for  measuring  time, 

68. 

gravity, 

W. 

70. 
virtual  length  of,  68. 
Pisa,  the  Leaning  Tower  of,  u. 
Plane,  the  inclined,  85. 

Water-power,  96. 
wheels,  96. 
breast,  96. 
horizontal,  97. 

INDEX. 


4OI 


Water  (continued) 

wheel  overshot,  97. 
reaction,  in. 
turbine,  98. 
undershot,  97. 
vertical,  96. 
Wedge,  the,  86. 
Weight,  4. 

of  bodies  in  air,  33. 

liquids,  21. 
Weight-lifter,  the,  31- 
Weights,  5. 


Wells,  Artesian,  19. 
Wheel  and  axle,  the,  77,  92. 
Wheels,  belted,  82. 

bevel,  82. 

cog,  81. 

crown,  82. 

friction,  81. 

spur,  82. 
Wheel-work,  80. 
Windlass,  the,  78,  92. 
Windmills,  95. 
Wind-power,  95. 


PART    SECOND. 


Abbe*  Nollet's  Globe,  380. 
Adiatnermancy,  210. 
Aldebaran,  spectrum  of,  115. 
Amplitude  of  vibrations  in  sounding  bod- 
ies, 7. 

Analysis,  spectrum,  112. 
Analyzer,  the,  135. 
Anion,  274. 
Anode,  274. 
Anthelia,  354. 
Atmosphere,  composition  of  the,  321. 

electricity  in  the,  347. 

heating  of  the,  321. 

moisture  of  the,  332. 

pressure  of  the,  32. 
Aurora  Borealis,  the,  352. 
Axis,  the  optical,  162. 


Balance-wheel,  the  compensation,  249. 
Battery,  Bunsen's,  272. 
Daniell's,  272. 
electric,  270. 
Grove's,  272. 
Leyden,  291. 
magnetic,  258. 
thermo-electric,  283. 
Beats,  39. 
Boiling,  226. 
Boiling-point,  the,  226. 

of  water  affected  by  cohe- 
sion, 228. 

of  water  affected  by  pres- 
sure, 227. 
of  water  affected   by  the 

vessel,  229. 

Brocken,  the  spectre  of  the,  164. 
Bunsen's  cell,  272. 


Calms,  region  of,  326. 

"  rain  in,  344. 


Calorescence,  200. 
Calorimeter,  the,  219. 
Camera  obscura,  the,  152. 

the  water,  153. 

Carbonic  acid,  condensation  of,  2  v- 
Cathode,  274. 
Cation,  274. 

Cells,  construction  of  voltaic,  271 
Charge,  distribution  of  electric,  290. 
Chords,  44. 
Clang-tint,  26. 
Clocks,  electric,  306. 
Clouds,  337. 

cirro-cumulus,  342. 

cirro-stratus,  342. 

cirrus,  339. 

colors  of,  356. 

cumulo-cirro-stratus,  342. 

cumulo-stratus,  342. 

cumulus,  340. 

nimbus,  342. 

stratus,  340. 
Coils,  induction,  299. 
Collodion  process,  the,  184. 
Color  of  bodies,  in. 
Color-blindness,  161. 
Colors,  analysis  of,  112. 

complementary,  no. 

in  crystalline  plates,  139. 

of  soap:bubbles,  116. 

prismatic,  106. 
Condensation,  231. 
Coronas,  354. 

Crystals,  biaxial  and  uniaxial,  128. 
Cupric  sulphate,  electrolysis  of,  274, 
Current,  heat  developed  by,  280. 
induction,  288,  299. 
intensity  of,  269. 
light  developed  by,  282. 
makes  iron  magnetic,  277. 
quantity  of,  269. 
resistance  to,  266. 
Curves,  magnetic,  256. 

D. 

Daguerreotype,  the,  183. 


402  INDEX. 


Dew,  334- 

Diathermancy,  193,  210. 
Diffraction  fringes,  125,  377. 
Discharge,  convective,  292. 

glow,  292. 

Discharger,  the,  291. 
Discords,  45. 
Dispersion  of  light,  106. 
Dissonance,  cause  of,  46. 
Distance,  estimated  by  the  eye,  163. 
Duboscq's  electric  lamp,  317. 


E. 

Ear,  the  human,  83. 

range  of,  84. 
Earth,  telegraphic,  311. 
Echoes,  12. 
Electric  battery,  270, 

clocks,  306. 

current,  263. 

lamp,  317. 

light,  282. 

telegraph,  308. 

wheel,  292. 

Electrical  machine,  285. 
Electricity,  a  source  of  mechanical  power, 

atmospheric,  318,  347. 
conductors  of,  268. 
developed  by  friction,  285. 
"  heat,  283. 
"  magnetism,  279. 
positive  and  negative,  288. 
voltaic,  263. 
Electrodes,  274. 
Electro-gilding,  306. 
Electrolysis,  274. 
Electrolyte,  274. 
Electro-magnets,  277. 

strength  of,  278. 
Electro-metallurgy,  306. 
Electro-plating,  305. 
Electroscope,  287. 

gold-leaf,  287. 
Electrotyping,  304. 
Energy,  actual,  358. 

mechanical,  358. 

converted  into  heat, 

358,  359- 
molecular  or  atomic,  358. 

"         converted    into    heat, 

358,  362.  , 

converted    into    elec- 
tricity, 358. 
muscular,  358. 
of  affinity,  358,  363. 

cohesion,  358. 
"  gravity,  358,  363. 
potential,  358. 
source  of,  363. 

transmuted,  not  destroyed,  363. 
Engines,  electro-magnetic,  317. 
Evaporation,  231,  333. 
Expansion  by  heat,  234. 

coefficient  of,  235. 
effects  of,  250. 


Expansion  of  gases,  238. 
"  liquids,  236. 
"  solids,  237. 
Eye,  the,  153. 

adjustment  of,  155. 
affected  by  age,  168. 
normal,  167. 

F. 

Farmer's  alloy,  283. 
Far-sightedness,  166. 
Flames,  naked  sensitive,  373. 

sensitive,  78. 

sounding,  74. 
Fluorescence,  200. 
Foci,  invisible,  199. 
Fogs,  335. 

Foucault's  rheotome,  301. 
Fraunhofer's  lines,  115,   197. 
Freezing-mixtures,  233. 
Friction,  always  rhythmic,  74. 

electricity  developed  by,  285. 

a 

Galvanometer,  the,  265. 

the  astatic,  265. 
Gases,  absorption  of  heat  by,  205. 


"  light  by,  114. 
>ound  in 


velocity  of  sound  in,  68. 
Gassiot's  cascade,  379. 
Geissler's  tubes,  303. 
Graham's  pendulum,  249. 
Gulf  Stream,  the,  241. 


H. 

Hail,  346. 

Heat, 'absorbed  by  gases,  205. 

"  solids  and  liquids,  204 
"  vapors,  208. 
causes  liquids  to  boil,  226. 

solids  to  melt,  223. 
conduction  of,  213,  214. 
convection  of,  240. 
converted  into  mechanical  energy, 

361. 

developed  by  electricity,  280. 
dispersion  of,  196. 
electricity  developed  by,  283. 
expansion  by,  234. 
from  affinity,  363. 
latent,  of  gases,  226. 

"  fiquids,  224. 

"  steam,  244. 
luminous,  193. 

makes  gases  more  elastic,  239. 
mechanical  equivalent  of,  361. 
obscure,  193,  199. 
of  the  atmosphere,  321. 
polarization  of,  197. 
quality  of,  204. 
radiation  of,  193,  321. 

"        "  explained,  210. 


INDEX. 


4°3 


Heat,  reflection  of,  194,  378. 
refraction  of,  195,  378. 
solar,  amount  of,  365. 

'     Helmholtz's  theory  of,  367. 
"    meteoric  theory  of,  365. 
specific,  216. 

found  by  melting,  217. 
"  mixture,  217. 
of  gases,  220. 
"  liquids,  219. 
the  same  as  light,  197. 
unit  of,  216,  360. 
Heating  by  steam,  244. 
Helix,  277. 
Hygrodeik,  the,  252. 
Hygrometers,  251. 


Iceland  spar,  128. 
Induction  coils,  299. 

electrical,  288. 
Inductorium,  the,  301,  380. 
Instruments,  musical,  51. 

stringed,  51. 

wind,  55,  72. 

Intensity  of  electricity,  269. 
Interference  of  light,  118. 

"  polarized  light,  136. 

"  sound,  35. 
Invisible  foci,  199. 
Irradiation,  159. 


Kaleidoscope,  the,  178. 


Lamp,  electric,  317. 

the  platinum,  207. 
Lenses,  148. 

achromatic,  173. 
images  formed  by,  149. 
Leyden  battery,  291. 
jar,  291,  380. 
Light,  absorption  of,  in. 

chemical  action  of,  182. 

composition  of  white,  108. 

diffused,  99. 

dispersion  of,  106. 

intensity  of,  94,  98. 

interference  of,  118,  126. 

length  of  waves  of,  123. 

origin  of,  124. 

polarization  of,  130. 

polarized  by  reflection  and  refrac- 
tion, 134, 

propagated  by  the  ether,  122. 

radiation  of,  91. 

reflection  of,  96,  1 19. 

refraction  of,  96,  99. 

total  reflection  of,  101,  377. 

undulatory  theory  of,  118. 

velocity  of,  93. 


Lightning,  349,  351. 
rods,  351. 

M. 

Magic  lantern,  the,  174. 
Magnetic  battery,  258. 
curves,  256. 
induction,  257. 
Magnetism,  255,  353. 

developed  by  electricity,  277. 

of  the  earth,  256. 

of  wire  carrying  a  current, 

278. 

Magneto-electricity,  279, 
Magneto-electric  machines,  293. 
Magnets,  forms  of,  258. 

making  of,  258,  259. 
natural,  257. 
poles  of,  256. 
Melting-point,  the,  223. 
Microscope,  the  compound,  170. 
"    simple,  170. 
"    solar,  176. 
Mirage,  102. 
Mirrors,  concave,  178. 
convex,  180. 
parabolic,  181. 
plane,  177. 
Mists,  335. 

Molecules  of  bodies  are  in  motion,  212. 
Monsoons,  327. 
Musical  sounds,  18. 

pitch  of,  1 8. 
transmission  or,  28,  29. 


N. 

Near-sightedness,  166. 
Nebular  hypothesis,  the,  366. 
Needle,  astatic,  265. 

dipping,  256. 

telegraph,  308. 
Nodal  lines,  26. 
Nodes  formed  in  plates,  25. 
"  strings,  23. 
Noise,  defined,  18. 

O. 

Octave,  defined,  22. 

Ohm's  law,  268. 

Opacity,  91. 

Opera-glass,  the,  174. 

Optic  nerve,  action  of  light  upon  the,  157. 

Optical  axis,  the,  162. 

Organ-pipes,  64. 

reed,  70. 
Overtones,  or  harmonics,  26. 

P. 

Parhelia  and  paraselene,  356. 
Pendulum,  Graham's,  249. 
Penumbra  of  shadow,  93. 
Phosphorescence,  201. 


404 


INDEX. 


Photographic  printing,  184. 
Photography,  182. 
Photometers,  95. 
Pincette,  the  tourmaline,  142. 
Pitch,  defined,  18. 
Polarization  of  electricity,  289. 
"  light,  130. 

circular  and  ellipti- 
cal, 136. 
rotatory,  137. 
Polarizer,  the,  135. 
Prisms,  96. 

achromatic,  107. 
double-refracting,  129. 
for  total  reflection,  101. 
Nicol's,  135. 

path  of  rays  through,  104. 
Purkinje's  figures,  158. 


Q. 

Quantity  and  intensity  of  electricity,  269, 
286. 


Rain,  343- 

in  India,  345. 
in  the  tropics,  344, 
Rainbow,  the,  144,  354. 
Rays,  93. 
Reed  pipes,  70. 
Refraction,  double,  129,  131. 

effects  of,  103. 

index  of,  101. 
Relay,  311. 
Resonance,  58. 

cause  of,  61. 
Resultant  tones,  40. 
Retina,  duration  of  impression  on,  159. 
exhaustion  of,  161. 
structure  of,  156. 
Rheostat,  the;  266. 
Rheotome,  the,  300. 

Foucault's,  301. 

Rods,  longitudinal  vibrations  of,  56. 
Ruhiakorff  s  coil,  301. 


Saccharometer,  the,  138. 
Saint  Elmo's  fire,  352. 
Scale,  the  musical,  49. 
Shadows,  91. 
Siren,  the,  19. 
Sirius,  spectrum  of,  115. 

Soap-bubbles,  colors  of,  no,  377. 

Sonometer,  the,  22. 

Sound,  caused  by  vibrations,  3. 

coincidence  of,  35. 

intensity  of,  7. 

interference  of,  35. 

passes  through  gases,  liquids,  and 
solids,  4. 

propagated  by  vibrations,  5. 


Sound,  quality  of,  26. 
reflected,  10. 
refracted,  14. 
velocity  of,  in  air,  8. 

"  gases,  68. 
"  liquids,  69. 
"  solids,  10,  59. 
"  "  water,  9. 
«*        "  "  wires    of    different 

kinds,  56. 

will  not  pass  through  a  vacuum,  3. 
Sounding-boards,  51. 
Sound-waves,  length  of,  21. 

superposition  of,  34. 
Speaking-tubes,  7. 
Spectre  of  the  Brocken,  the,  164. 
Spectroscope,  the,  112. 
Spectrum,  the  solar,  105. 

analysis  of,  1 12. 
chemical   action   of, 

185. 

reversed,  114. 
Spheroidal  state,  the,  230. 
Steam,  heating  by,  244. 

latent  heat  of,  244. 
Stereoscope,  the,  165. 
Storms,  328. 
Strings,  vibrations  of,  22. 

"  laws  of  the,  53. 


T. 

Telegraph,  Bain's,  308. 

combination  printing,  308,  31 
fire-alarm,  315. 
four  things  essential  to,  308. 
House's  printing,  312. 
Hughes's    "         3x3. 
Morse  s,  308. 
needle,  308. 
submarine,  316. 
Telegraphic  alphabet,  Morse's,  310. 

earth,  311. 
Telescope,  the,  172. 

"    reflecting,  181. 
"    refracting,  181. 
"    terrestrial,  173. 
Temperature,  215. 

affected  by  drainage,  334. 
affects  time-pieces,  249. 
of  the  atmosphere,  321. 
Thaumatrope,  the,  159. 
Thermo-electricity,  283. 
Thermometer,  the  alcohol,  247. 
"  air,  247. 
Breguet  s,  248. 
differential,  247,  284. 
mercurial,  245. 
scales,  246. 
Thunder,  350. 
Thunder-storms,  349. 
Tones,  resultant,  40. 

summation,  42. 
Tornadoes,  329. 
Tourmaline,  and  its  action  on  light,  133. 

pincette,  the,  142. 
Trade-winds,  325. 


INDEX. 


405 


Transparency,  91. 

Tubes,  vibrations  in,  63,  64. 

Tuning-fork,  the,  18. 


U. 

Umbra  of  shadow,  93. 

Undulatory  theory  of  light,  the,  118. 

V. 

Vibrations,  longitudinal,  55. 

of  columns  of  air,  63. 
sympathetic,  31. 
Vision,  laws  of,  166. 

near  and  far  point  of,  166. 

single,  161. 

Visual  angle,  the,  162. 
Voice,  the  human,  80. 
Voltaic  arc,  the,  281. 

electricity,  363. 


Voltaic  pair,  the,  263. 
Voltameter,  the,  276. 
Vowel  sounds,  81. 


W. 

Water,  irregular  expansion  of,  243. 

specific  and  latent  heat  of,  242. 

Water-spouts,  332. 

Water-waves,  superposition  of,  33. 

Watery  vapor  in  the  air,  332. 

elastic  force  of,  335. 

Weights  and  measures,  French,  370. 

Wheel,  the  electric,  292. 

Whirlwinds,  329. 

dust,  330. 

Wilde's  magneto-electric  machine,  296. 

Wind  instruments,  55,  72. 

Winds,  324. 

of  Asia  and  North  America,  327 
"  middle  latitudes,  326. 
"  northern  Atlantic,  339. 


i'HE     END. 


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